This is very risky
First, its not that easy to break the game with a rule change. Even in the existing rules there is a good amount of power variance, and that may be a good thing too, as it gives players something to explore and discover as they become more expert in the system.
For a change to really break something, it typically needs to that feature being so powerful that it overshadows other approaches, and leads to repetitive play patterns, or so weak nobody is using it, and the class that gets the change becoming unattractive to play. You also need to look at how it can be abused in a focused build, because even if it is fine in others, that is how someone will use it.
Reasons this might be fine:
First, the change is somewhat symmetrical. It will benefit monsters with crossbows, as much as players. Players of course can use it all the time, and most monsters do not have them (at least, as given in the MM), so it will benefit players more, but at least it's possible to be used against them.
Second, it's open to many. Light crossbows are simple weapons that pretty much everyone can use, so it will not enhance just one class and make it better. It still of course favors a build that wants to use a ranged weapon more.
Third, there are other ways to get advantage on attacks, although many of them are harder to engineer than simply dropping prone: you can attack from being invisible or in darkness with devil sight or by being a gloom stalker ranger, or have your familiar or some minion use the help action.
Forth, and most importantly using it has a cost: when you drop prone, you sacrifice mobility. It will be harder to get away if someone gets close, and anyone who manages to get within 5 feet also has advantage to hit you.
Still, I think this is risky: advantage is a big swing approximately worth +4 or +5 to hit, and your optimized crossbow expert and sharpshooter fighter always attacking with advantage to add +10 to damage at no real cost can be quite overpowered. With crossbow expert, they even get an added bonus action attack to make it worse. It will be easier and even more problematic than other ways to do exploit sharpshooter with advantage, and a build exploiting sharpshooter with advantage nearly broke our game.
Your motivation is verisimilitude. By that measure, if you think about how crossbows were cocked in the real world, with belt hooks and such, it may be easier to aim, but it also might be harder to reload the crossbow.
I would at least exclude hand crossbows from this, and state that you cannot avoid the loading cost if you do this, so crossbow expert builds will not exploit this to unbalance your game.