Does being punished reduce the chances of you getting keys?

Yes, getting punished reduces your chances of getting Hextech Loot to 0 while you're in your reform period.

The key punishments are so stupid. "You've finished your punishment, now you will continue to be punished for an infinite amount of time without keys until your behavior improves, young man".

There's no point in being nicer or less toxic when one premade will get you the ban and it could be months until you get keys again.