Paying for commute expense is already a solved problem.
Some examples, a fixed amount based on data provided every month for commute. (200 dollars a month or whatever)
Or if a company wants to be both stingy and generous at the same time, make you expense your gas or public transportation every month up to a certain limit.
It doesn’t matter if you move to a different part of town. The cost is negligible to a business.
Bosses and workers still can’t agree on whether the commute is part of the work day, and it’s creating a $578 billion productivity problem ( fortune.com )