Overall, I think this is probably an improvement to the game. The start of combat in 5e is one of its worst systems, and anything that makes that go faster is probably a Good Thing. Like any house rule, it needs playtesting.
I have played with a similar house rule (which I'll include at the bottom of my answer) to great effect.
There's two parts to this answer; I'll start with the objective balance considerations.
Overall, initiative is usually not a big deal in 5e
Fifth edition D&D has done away with a lot of the "rocket launcher tag" mechanics from 3.5e, such as save-or-die effects. Most battles last for several combat rounds, so the characters who act first don't necessarily get to take many more actions than the characters who act last. There's a couple of things still worth mentioning, though.
Some class features grant (partial) proficiency to initiative already
I don't have my rulebook with me right now, but IIRC, the Bard's Jack of All Trades feature would allow them to apply half their proficiency bonus (rounded down) to initiative rolls. After this change, every PC is now getting their full initiative, so the Bard is slightly nerfed by comparison.
Some spells care a lot about whether certain characters have moved
Some spells, like Fireball or Prismatic Wall, are optimal if nobody has closed to melee yet. Others, like Haste, are optimal if the recipient of the spell is going to get a turn before the enemies force the caster to make concentration checks. Command works best if the enemy just acted and is going to be prone (giving your teammates advantage on attacks) for everyone else's turn before it has a chance to stand up. The list goes on.
PCs can get locked into the "wrong" order
If the wizard always goes before the fighter, then the wizard can reliably land a Fireball on the enemy group before the fighter advances to melee to attack. If the wizard never goes before the fighter, then Fireball becomes a much less useful spell - the wizard might not be able to catch the entire enemy group without also roasting their friend.
Normally, everyone can expect to have some encounters where they do well and some encounters where they do badly. Reducing the variability here means that the wizard could have either very many or very few opportunities to show off and be powerful.
This will make PvP a lot worse if you allow PvP (and apply this rule to it)
Player-versus-player combat will be a lot more predictable if the initiative is rolled ahead of time. In my experience, this is a bad thing because a lack of uncertainty means that the expected winner can bully the expected loser. The easy fix to this is to commit to normal initiative if PvP happens, or ban PvP combat completely.
The other thing to consider here is what this does for the pace of the game.
Players like to roll dice
YMMV here, but in my experience, players like rolling dice. Rolling dice keeps them in the game even when they aren't making decisions. The DM rolling dice is less thrilling. If I need a die rolled, I try to find excuses to have the players be the one to roll it. My games run better if the person who's on watch rolls for random encounters, etc.
This house rule means that at the beginning of combat, there's a bookkeeping-heavy moment (establishing the initiative order) where the players haven't rolled any dice. This could throw the players out of the action...
This will probably make start-of-combat happen a lot faster
The transition into combat is (in my experience) one of the worst parts of D&D. It takes something that should be exciting - the moment at which the stakes of a scene get escalated to include injury and death - and pauses the game for a couple minutes of bookkeeping/roll-call before play can continue.
This house rule eliminates that down beat, and that gameplay improvement alone probably trumps all of the other considerations here, at least when compared to RAW.
A similar rule: Initiative Tests
At my tables, Initiative works like this:
- During design time, I set an "Initiative DC" for each encounter.
- At the beginning of each encounter, the PCs all make an initiative check against the initiative DC
- PCs who beat the initiative DC then take their turns (they choose what order to act in*)
- Then the monsters take their turns (in any order I choose)
- Then all PCs take their turns (in any order they choose*)
- Go to step 4, repeat until the encounter is over.
- If there's a dispute where more than one PC wants to go first, I have them roll an opposed Initiative check. In my experience, most encounters pass without any such disputes.
This is a very similar rule to yours; only one side rolls initiative, while the other has a fixed initiative score. The differences are:
- The players roll dice, versus the GM rolling dice
- The players choose what order to act in, versus always acting in a fixed order. (Monsters do the same)
- The DM doesn't need to track turn order, but does need to make sure no one goes twice in the same turn (since they're going out of order).
- Conversely, asking "Who wants to go next?" sometimes breaks the rhythm of play if no one has figured out what they want to do, while your rule preserves a single answer to that question.
- Mine doesn't give proficiency to initiative, but allowing combatants to choose their order of operations is a more significant advantage for PCs than monsters most of the time.