I guess you would have times where the umpire doesn’t report but they seem to do it quite often already even in instances where a report is not necessary so I don’t feel like you’d miss too many cases.

That would cause the opposite issue then of players being removed when they shouldn’t be.

Honestly it would be better if they missed cases and only sent off the most egregious examples. Umpire’s jobs are already difficult and they often make mistakes because of that difficulty. An incorrect free kick is a lot less impactful than incorrectly sending a player off.