I mean, if you go many days without actually producing anything, then presumably you will be let go from the company.

This is already a de facto advantage for people that are closer. Lack of commute often means lack of stress, which leads to more productivity, which leads to promotion.

Clearly none of it is guaranteed, but that general markov chain works surprisingly well. If the company can't pay enough for you to live close, that is already a drain on the company. Whether they realize it or not.

No, you have to swipe your timecard at the office when you arrive and then get going on your commute back home.

Yes. This. :)