Asking middle and especially lower class people to pay more for energy, even just in the short term, runs the risk of turning them against eco-conscious legislation.
It's not just about the ones that can't afford to pay more for the energy, there also usually isn't a viable alternative available for them to even look at moving toward instead. It's one thing to make a decision pay more for convenience, if you have another option. If there is no other option, you just feel like you're getting personally fucked.
In the US, all of the public transit infrastructure outside of like 4 major cities is dogshit. There may be a bus, that doesn't go everywhere, runs at odd times, and is poorly maintained. Technically available, but if you need to travel across town to work, takes 3 hours one way to do so through 2 different transfer stations. And since everything was built around personal vehicles, things are also not within walking distance even if you are lucky enough to work from home or have something closer.
Having a car is a necessity for most of the country. Without having viable alternatives, increased fuel prices aren't going to actually fix anything, just turn people even more against any changes.
This is why things like EVs are a good middle ground with the current lack of public infrastructure available nationwide. It's an easy drop in replacement that's a better ongoing option, with a side effect of also costing less to maintain along the way.