Exactly. Too few people understand economics, that current costs are being brought down by offsetting future costs.
The same with any pollution in any industry. If the industry is allowed to follow bad practices, and cause pollution but not deal with it, then they are not bearing the brunt of the full costs of generating that pollution. Someone has to clean it all up eventually, typically the government, then people complain about taxes.
You can complain about taxes, but you just voted for someone to cut regulations on industry which then causes the pollution which needs tax dollars to clean it up.
(I know CO2 is not a 'pollutant' technically, it is just another example of the 'cost' to the environment is not being allocated correctly to the producer. I feel need to be correct since even using the word 'pollutant' is a right wing argument point on why climate change advocates don't know what they are talking about.).
If the costs of current living standard wasn't externalized to future generations (to the detriment of the environment), they couldn't afford those bills to begin with.
Unfortunately, it's very hard to reduce people's living standards once they got used to it. So yes, the end result is what you're saying - however, I think it's a very important nuance. It was always a card house; we just chose to ignore the issue and continued to build on top of it.