Not a popular opinion, and it does suck, but I do think we should strive to sponsor mileage of any kind as little as possible and that includes employers paying for commute, to incentivise wirking closer to your home or relocating closer to your work
In the US, zoning restrictions means people literally cannot live very close to their jobs in a lot of locations because housing is far from businesses. City structures encourage commutes, and would require spending money to undo those problems. Your suggestion punishes the poor who would need to move more often to find new jobs.
We should instead sponsor more mass transit accessibility and frequency to decrease the use of single occupancy vehicles in daily commutes, which would have a for larger positive impact over trying to force people to live in specific locations that limit their ability to find work. For example, if people move near their jobs and want a different job, making them movie again is stupid when instead they could have easy access many potential jobs within 30 minutes or less on public transportation if working at home is jot an option.
Yes well, unfortunately, hastening climate change will also disproportionately punish the poor in very concrete ways much more than high gas prices ever will. It'll also punish the real poors of the southern hemisphere.
You can force corporations to pay 50% of the fare of any of their employees transit like it's done in a lot of places in Europe and I'm not against that as a band-aid but nothing beats re-zoning to fix your density issues and living close to work in terms of quality of life and ghg emissions