Of course, those whose fuel consumption isn't as efficient, or who travel further would be much harder hit. I doubt that wages would rise the same amount, let alone rise proportionally to cover such an expense.
Yes, it would encourage people to either not drive as much, as far, or in as big vehicles - but what knock-on effects would that have? Long distance freight would obviously be impacted, although that might be buffered somewhat by efficiencies of scale - a very large vehicle may be able transport more for a given amount of fuel. Say goodbye to small transport, though. And, perhaps, say goodbye to Just-In-Time transport.
As a crisis develops, there are obvious ways to adjust, given enough warning and wisdom. More postal depots, fewer deliveries. Encourage mass-transport. Reduce the distances things are transported. Fewer large distribution hubs, more smaller ones. Less out-of-season produce, transported large distances, or a much higher premium on doing so.
Of course, this relies on societies moving away from current systems.
Governments often dislike investing in a high quality public transport system. We like cities divided into residential, commercial, and industrial. Cars are a hard habit to break - I will admit to this, although if I was living in the city, I would go back to riding a 50cc scooter most of the time.
There used to be rail near where I lived. There is, in fact, a rail line that still exists in parts, that ran a mile or so (directly) from me. The line hasn't been used in years, is missing large sections, and is in disrepair generally. Whether the local government has any interest in getting it back into condition is another question. Giving warning, they might - the old line went a few dozen miles further on, to a small town that supplies local beef - slaughterhouse and all - as well as some other produce. If road transport became increasingly costly, would they have the time, inclination and resources to find alternatives?
I guess that is what prepping is, really - finding alternatives.