Aborting won't give them more whites, since aborted games don't count towards the color history and the site attempts to balance color allocations.
What will happen is that the player that does it a lot will get restricted and they will no longer be able to abort, only resign. They will also get placed into a pool of other players that do the same thing.
https://support.chess.com/customer/en/portal/articles/1444922-fair-play-policy
The vast majority of games in which my opponent aborts are when they are black. It seems a lot of players are aborting when black to give themselves a disproportionate number of white games.
Also some players will feign a disconnect and run down their disconnect timer to just a few seconds in the hope that you'll bail ship before then, then do a sneaky last second move. For short games this is very annoying.
Maybe use statistical analysis to find abusers and give them a shorter auto-resign timer?