I'm considering this house rule because at level 2 a rogue gets Cunning Action, yet a monk must pay for a very similar privilege from a very limited pool that the typical monk would often prefer to use for something else.
I don't think it would cause a serious balance problem, especially if you are generally letting the players rest between each fight. However, it does make the monk significantly more damaging at very low level -- he still can't flurry and disengage in the same turn, since they're both bonus actions, but it just means that many more rounds with a flurry.
By the time he's at level 5 or 6, it's not so much of a big deal, because he'll have enough ki points to use one just about every turn without running low anyway.
That said, I'd tend to fall on the side of leaving the class alone unless you see an actual problem at the table. Rogues are more mobile and skillful, typically, but have to work to set up advantage to use their sneak attack, while monks move faster and have a lot of weird combat tricks, but have limited use out of a lot of their techniques. It doesn't seem unbalanced to me as written.
I think you will be fine if you follow the DMG's recommendations on short rests
From my experience playing as a Monk through Curse of Strahd (specifically Open Hand), I find that Monks in 5e fulfill an odd role compared to the other classes. After 5th level, they're able to make a lot of small attacks, but don't have big single-target damage, so they're not really a striker; they aren't particularly good at being attacked directly, so they're not a tank; they can't deal area of effect damage easily, so they're not your arcane caster; and they can't heal others, so they're not the party healer. My best description from them would be what I've coined 'party enabler' due to Stunning Fist. Similar to a 4e controller type, they can attack an area with a lot of small attacks and force saves on debilitating effects. Once they hit 5th level, they excel at stun locking casters, but even then they usually need someone else to deal the damage.
With that in mind, let's consider their effectiveness at controlling things to assess the balance of your proposed change for an average fight. I'm only going to evaluate things to 10th level since that's the extent of my experience. For the purposes of this evaluation, I am going to assume the fight lasts 6 rounds, the movement is maxed out every round, no OA occur, no crits, and the Monk is 10th level with the following:
- 50' movement speed
- 1d6 Martial Arts damage for all attacks
- 10 ki points
- No feats that increase damage (this just makes things really variable)
- 18 Dex, 16 Wis, 14 Con
- 73 hit points
For comparison, vs a ranged Rogue who is 10th level with the following:
- 30' movement speed
- 1d6+1 Shortbow +1 damage for all attacks
- 5d6 Sneak Attack and the means to do so every round
- No feats that increase damage (though Sharpshooter can be a nice way to bump up damage)
- Ignoring archetype features
- Uncanny Dodge
- 20 Dex, 14 Con
- 73 hit points
I will assume that every round, the character is hit with 2 attacks, one that deals a base 4d8 (18) damage and requires a Dex save that they both succeed on half the time and a second attack that hits and deals 4d10 (22) damage if they are in melee range.
Way of the Open Hand These Monks are fantastic at getting into an enemy's face and delivering a quick flurry of blows that force multiple saves or else bad stuff. The drawback to this tradition, though, is built into initiative. If your allies all go after you, then they can greatly benefit from an enemy that been knocked prone or can't take reactions, otherwise, you get almost no benefit besides a few extra hits for base weapon damage.
Assuming the initiative order doesn't betray you, being able to get off one or two extra flurries per fight isn't likely to make a huge difference in the grand scheme.
Assuming the Monk uses Step of the Wind every other round to leave melee range safely, Flurry of blows on the other rounds, and Stunning Fist once per round, we find the following:
- The Monk travels 300 feet during the fight (50' per round);
- The Monk makes 16 attack rolls during the fight, assuming they all hit, the Monk deals 120 magical damage (20 damage per round);
- The Monk forces 4 saves vs knockback or prone effects;
- The Monk forces 5 saves vs stun effects
- The Monk leaves the fight with 0 ki points remaining, running out in the 5th round.
- The Monk takes 93 damage over the fight (22 damage on each of the 3 rounds they did not use Step of the Wind, 9 damage on each the 3 rounds they failed the Dex save)
For comparison, a Rogue that hits a sneak attack once per round and uses Cunning Action every turn to leave melee sees the following:
- The Rogue travels 180 feet during the fight (30' per round);
- The Rogue makes 6 attack rolls during the fight, assuming they all hit, the Rogue deals 132 magical damage (22 damage per round);
- The Rogue does not cause additional effects beyond damage with their attacks;
- The Rogue takes 27 damage over the fight (0 damage versus the melee attack because they did not end any turn in melee, 9 damage on each of the rounds they failed the save)
Summary: Using their ki frequently, the Monk is just short of the Rogue's damage over the course of the one fight and probably cause some significant status effects (assuming initiative is favorable), which will help to spike the damage rate of the Monk's allies. However, without outside healing or resorting to Wholeness of Body, this Monk is downed probably in the 5th round, also the same time this Monk runs out of ki. The lack of ki means the Monk will not be able to contribute nearly as fully in another fight without taking a short rest.
Way of Shadow There's really not a lot of difference for a Shadow Monk with this change. Their Shadow Step feature already requires them to use a Bonus Action, so there's no real change for them. Being able to have a little extra ki to fuel their other features can improve their ability to spy and sneak more effectively, but I've yet to see any of the spells in the Shadow Arts consistently change the tide of a combat; at best they alter how things have to move around within the fight.
Regardless, most of those spells in Shadow Arts require concentration, so letting the Monk get off one more in a combat probably isn't going to suddenly make a huge swing of things into unbalanced territory.
Assuming the Monk uses Shadow Step every other round to leave melee range safely, Flurry of blows on the other rounds, and Stunning Fist once per round, we find the following:
- The Monk travels 330 feet during the fight (55' per round);
- The Monk makes 18 attack rolls during the fight, assuming they all hit, the Monk deals 135 damage (22.5 damage per round);
- The Monk forces 6 saves vs stun effects
- The Monk leaves the fight with 1 ki points remaining.
- The Monk takes 93 damage over the fight (22 damage on each of the 3 rounds they did not use Shadow Step, 9 damage on each the 3 rounds they failed the Dex save)
Summary: Pretty much the same as the Open Hand Monk, but it's worth noting that the Shadow Step feature gives many of the disengagement features sans ki costs. As a result, Shadow Monks gain substantially less from your proposed change compared to other monks.
Also, this Monk is also likely downed around the 5th round as well and doesn't have an inherent healing feature to fall back on.
Conclusion One of the big differences between Monks and other classes is that Monks almost always have a use for their bonus action in the form of an extra attack. Step of the Wind and other ki features expand that list of options, but at the end of the day, the Monk only has 1 bonus action per round and it's use is usually split between living for tomorrow or dealing a bit more damage today.
If you follow the DMG's recommendation for short rests, you will probably be fine with your proposed house rule. Monks will see a little bit of a bump in their normal damage per round because they will have more access to their Flurry of Blows, but it shouldn't make a substantial difference once you hit the mid levels. On average, you will also probably see the party's damage output as a whole go up a bit due to status effects, which can be a lot of fun for a table when they get to work together effectively. As their damage output will still be controlled by the availability of ki, they may be able to keep pace in damage output with other striker classes to a point, after which their damage drops off significantly. As a result, the player will still have to consider conserving their ki because once it's gone, they're pretty much a guy that brought his fists to a dragon fight.
If you think short rests will be regularly allowed after every fight, then it's likely better to keep things as-is otherwise Monks will probably be outshining Rogues for damage on a regular basis.
If you go this route, I would consider buffing the Shadow Step class feature in some manner if you do elect to go this route as a means to not have it unintentionally nerfed by virtue of the proposed buff. Maybe the character has 60' of movement they can use for teleportation purposes for that feature; thus they could teleport in and back within the same turn.
I play a subclass of monk from "Heroes of the Orient" (it's from dmsguild). For this subclass, you choose a magical tattoo every time you would get a subclass feature (goes up to 5 tattoos by level 17). One of these is the Heron tattoo that makes your step of the wind feature permanent and cost no ki points.