This is a difficult question to answer, because there are a lot of moving parts for class features that you want to identify. To answer this, I'm going to break down each aspect into simpler parts.
First, Deflect Missiles:
Starting at 3rd level, you can use your reaction to deflect or catch the missile when you are hit by a ranged weapon attack. When you do so, the damage you take from the attack is reduced by 1d10 + your Dexterity modifier + your monk level.
If you reduce the damage to 0, you can catch the missile if it is small enough for you to hold in one hand and you have at least one hand free. If you catch a missile in this way, you can spend 1 ki point to make a ranged attack (20/60 feet) with the weapon or piece of ammunition you just caught, as part of the same reaction. You make this attack with proficiency, regardless of your weapon proficiencies, and the missile counts as a monk weapon for the attack.
Spend your reaction to reduce incoming ranged damage, scaling with how strong you are. You can also spend a Ki point to attempt a ranged attack if the incoming damage was weak enough.
Now, the Grappler feat:
Prerequisite: Strength 13 or higher
You've developed the skills necessary to hold your own in close-quarters grappling.
You gain the following benefits:
- You have advantage on attack rolls against a creature you are grappling.
- You can use your action to try to pin a creature grappled by you. To do so, make another grapple check. If you succeed, you and the creature are both restrained until the grapple ends.
You need strength for this feat. You hurt enemies more when they're grappled(uses strength), and you can do a super grapple which effectively paralyzes you and a bad guy.
- The monk will lose out on a way to spend their reaction. What other ways could a monk spend their reaction on a regular basis?
- Answer: Slowfall, Subclass abilities
- The monk will have fewer means of dealing with ranged attacks. What other ways can monks deal with ranged attacks?
- Answer: Nothing other than standard AC and movement
- Grappling uses a Strength (Athletics) check against the opponent to succeed. Does the monk utilize Strength?
- The monk will be restrained when using the "super grapple". Do they have the protection they need to fight while restrained?
In most circumstances, this is very unfavorable. Monks generally do not use Strength, which is a core component of grappling. You could decide to allow Dexterity for grappling with this feature change.
But the key component is the lack of ranged defenses. Monks can only run and punch. They do not have many means of spending their reactions. They will take more damage, and they're already known for being fairly fragile compared to other melee fighters, especially if they're grappling someone.
Is to either keep things as they are, or incorporate grappling as a defensive maneuver with these changes.
Consider making ranged attacks against you have disadvantage while you are grappling. This would result in an average of -5 to hit you with ranged attacks while grappling, where Deflect missiles prevents 6-30 damage (Depending on stats). This would make it reminiscent of prior editions, where "shooting into melee" was a common concern for ranged attackers, as they would receive penalties for attacking targets engaged in melee combat (since it's hard to shoot a specific target in the frey).