It's not false equivalence

It very much is. You're equivocating alcohol and child abuse.

it's negation of your logic

Nope. Just because cops arrest child abusers doesn't mean that they're the only answer. In fact, a well-funded social safety net is much better at discovering and stopping it and most if not all other societal, psychological and psychiatric problems than cops will ever be.

but different.

Well, at least you got that part right 🤷

I might have put down, some people want to get drunk and beat you up, and the police is in the way of that too, now unless you are into that you provably don't want to get beaten up by drunks

Another case of giving cops credit for something that they do by default even though their way of dealing with it is much WORSE than alternative ways less focused on use of force and punishment as a deterrent.

The crime doesn't matter

It very much does, as treating every societal problem with the same blunt tool is an awful idea

get the point across that your reasoning as to why ACAB is flawed

Overly simplified for the sake of brevity, maybe, but otherwise nope, wrong again.

meaningless point farming

This might be difficult to understand to someone whose opinions are unpopular because they're bad, but sometimes people express honest opinions that other people agree with, rather than playing pretend for points.

The crime doesn't matter

It sure does.

women were getting the shit beaten out of them by their drunken husbands. So a huge number of people, especially women, thought prohibition would stop that

They thought wrong. Typical of conservatives to blame something external and simple for a societal problem rooted in toxic gender roles and family structures.

the cause was a lot more noble than people give it credit for.

Except for the fact that there's nothing noble about jumping to conclusions and trying to solve the only tangentially related problems of some by depriving everyone else of something that most of them enjoyed more or less responsibly.

a reason people don't understand now

On the contrary: we still understand that domestic violence is awful and we now also understand that alcohol doesn't in itself cause it.

A lot of people don't know that Abraham Lincoln was a big proponent of prohibition. It was seen by progressives as an important step to move society forward.