Ultimately the DM has to roll with the punches, and in most groups, as long as they are reasonable, it usually works out. For example, if the rogue came to me later and said "hey I want to get dex for grapple too!"....that's probably a no.
This has an action economy limitation, to do a grapple, the character is giving up something else (aka damage). So if a player is playing a grappling concept, than they are effectively trading 1 aspect (damage) for another (control). If the dm finds that reasonable, allowing the character to be good at it doesn't create a lot of power creep. From my experience with 5e grappling so far, if a player wanted to grapple all of the time as opposed to doing damage, I don't think that would be the least bit overpowering. And if they only used it very sparingly, well then the houserule didn't make much of a difference anyway.
See, the conflict between your two posts is one of the thing that bothers me about making a significant rule change for a particular player's character. On one hand, you argue that this is reasonable and that it's not the least bit overpowering - but on the other hand, if another player wanted to use DEX instead of STR for grapple, you'd probably say no. Well unless he does it at character creation time and says that his concept is 'a wrestler using the rogue class'. What if he takes a level of monk to make his concept work? Well then he'll probably be accused of being an Evil Powergamer for "absuing" the rule you added, since that so often what happens in this kind of discussion.
The problem I have is not with the raw power level destabilizing the campaign; dropping an extra feat or some attribute points on a character isn't going to completely break power levels and ruin encounters forever. The problem I have is that the players are creating their characters with a different set of rules, and that the rules are changing after the fact, and in a way that doesn't appear to be based on game balance or world logic. Also, while in the specific, single case, there's a good chance that no one was bothered, when you use ad hoc changes frequently the odds of someone feeling screwed by them goes up tremendously - and according to the OP this was not a consciously decided house rule, this is a 'just started doing it, and now that's how we roll' type of rule.
If a player came to me and said "I've got this idea for a rogue wrestler guy"...and his plan was to use it a lot, than I might be on board. And of course if that was the concept, but the second combat starts he does nothing but pull out the bow and sneak attack....well we may need to discuss.
This highlights why I'd prefer rules instead of ad hoc 'character concept' oriented exceptions. The idea of an agile character who sneaks around sniping with a bow but his face responds with BOOM TAKEDOWN when an enemy gets in his face instead of running away sounds like a lot of fun to me. I would like to build my wrestling guy then have him interact with the game world in a way that makes sense to ME based off of his personality and events that happen, as that's role-playing, and having a "we may need to discuss" moment because I'm using a common class feature in a sensible way means I'm not actually getting to control my own character's actions without an argument with the DM! I would much rather have rules for what a character can do and then do it, then have to ask for an exception to core rules and worry about 'we may need to discuss' if I'm not playing the character exactly as the DM has decided my character should act. (If the DM is going to take that degree of control, he can play the character and I'll get into another game).
People present these kind of ad hoc rules as player empowering, but from what I've seen in practice they tend to have a bunch of hidden strings like 'oh, since you have this, you have to use this at a certain exact frequency that I won't tell you. too much and I'll decide it's unbalancing, too little and I'll decide you're not fitting your concept' or 'Jimmy can use this, but you're bad if you ask to use it on your character and I'll say no and hold it against you even though it's more effective for him than it would be for you'.