It would be great if governments decided they should instead.

No, it wouldn't. Everyone would have to pay the taxes for that, but not everyone drives a car. Also, there would be no incentive to use cheaper transportation.

In other news, it would be great if I could eat for free and didn't have to pay rent.

If you are mandating to be in office and there are obvious expenses to be in office, like gas and car maintenance, then company should pay these expenses or stop mandating presence in office.

There would be every incentive to use the most optimal transportation (up to and including remote work) if business minded people were the ones bearing the cost.

In fact, a lot of companies throughout Europe do. Either through a fuel card (when leasing a car) or a travel allowance (which can either be used for gas or public transport).

Some governments, like in the Netherlands, also allow a percentage of travel costs to be deducted from yearly tax if a employer does not reimburse costs directly.