> I'm in Europe and I'd happily wear a jacket and a winter cap indoors.
That's the theory. Here is probably what would happen in practice: all the people that have disposable income will swallow the cost. All the people who can't swallow the cost will pour in their last savings for a few more hours of warmth. Those who can't will start rioting, especially when their children start coughing. It's hard to tell your child "put on a jacket, dad can't pay to keep you warm" when little Jimmy next door goes to a Safari next easter. There is only so much inequality you can accept before resorting to violence. I think it's better to ensure everyone can - at least - eat, sleep, keep warm and get some access to some entertainment.
> And people could go by bus, subway, ride share, so less oil and gas needed for transportation.
In practice, many people just can't do that. Either because those transport options do' not work or aren't ready yet. Think of Mr. Electrician who goes around the city in his van fixing peoples home. If he is forced to take the bus, he needs to reduce his client base to what's accessible by bus, he can do less client per day. Or he can pay for the gas and keep his activity. Or he can just let it go and ask for welfare, increasing the burden on social security for someone who is perfectly willing, able and qualified to work if not for high gas prices. Many low earning workers will have to make a choice between going to work, and going to unemployment. We have already started to see people making that choice with the current gas prices.
Of course, highly qualified profile who are already well paid will negotiate with their employers so that the companies swallow those added costs. Most companies will have no choice but to agree. So the people on the roads will be in the "already rich" category.
All in all, this would just increase the disparity between the upper and lower class. The upper class will swallow those cost by just saving a bit less, but generally keeping their lifestyle. The lower class will be hit the hardest, by having their spending power reduced and/or being moved to unemployment. One of these groups will benefit more of the economic recovery if/when prices goes down - you can guess which one.