I think “we” do, but we don’t quite care as much about future generations as we like to think we do. Especially not when others today are disproportionately benefiting.
If you tell me to deprive myself of some conveniences because some people in another part of the world in another decade/century will suffer as a consequence of my actions... I agree with the selfless option in theory, but in practice I will usually choose the selfish option.
I think humans have a hard time with sustaining independent action. If you knew that everyone around you was going to be deprived of some convenience, say a restriction on driving to every other day (like they do in some countries based on the last digit of your license plate), I think it'd be easier to accept and adhere to for a long duration. I think this is both because you know the burden is shared, but also because the impact of a large adherence will tend to be more measurable.
If, on the other hand, you independently decide to stop driving your car because you know the world is getting smothered with carbon dioxide, but see people daily driving modified diesel pickups belching smoke into the sky, you're going to feel a bit like you're pissing in the wind even trying.