Germany kind of does that... When you file your taxes, you claim the "Pendlerpauschale", which is, roughly translated, the commute lump sum. For the first 20 kilometres between home and work, people get 30 cents per km, any km after that gives you 38 cents.

It kind of works in the sense that the money you spend to get to work is more or less evened out. It is also paid regardless of your means of transport, so cheaper means (such as bicycles or trams) are incentivised by potentially making you some money in return. However, this is still far from an hourly wage... We're talking about a few hundred euros, maybe a few thousand per year if you have a long commute.

If you used the median time and would force employers to pay a wage I really don't get how you would either prevent people to move further away (if you have worker protection laws) or people being fired for living too far away (if you live in the USA). This would also make it far more profitable for higher incomes to commute, which seems kind of counter-intuitive as they are probably the ones who need it the least and who would be able to just move to a new home if they wanted to.