That already exists but it is for habitual offenders.
https://support.chess.com/customer/en/portal/articles/1444922-fair-play-policy
temporal ban after aborting a game
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It's bad enough that they do it to habitual defenders. It used to be much worse too. I used to play at school when I was 15 and I was consistently having issues with aborts, so much so and so unfairly that mods would clear me of it on a regular basis. Abort protection is, all in all, a garbage system that needs to be seen less. Not more.
I think it might be a good idea to block players from playing for like 5 min when the aborted a game in order to prevent people from abusing the abort function (like sniping for white, preventing specific openings etc.).