Me and my partner were discussing this yesterday, we always wanted 2 (don't have any currently) we thought to maybe hang fire a couple of years to see If they do have preventative measures to slow/ stop global warming first, however will likely have one.
I think the difference comparing it to the fear of bombs / wars is different as that is something that is in the hands of people and therefore isnt guaranteed to happen. Where as global warming is guaranteed to happen unless significant changes to our way of living are made.
I do think humanity will prevail in some way or another, but unless changes are made things may get very grim, wars over land as increased areas become uninhabitable from floods/fires/loss of crops/drying out of water. World hunger will increasing, poverty etc.
Even without the risk of global warming, I think jobs are going to be harder to come by with so much being automated, school places are already a struggle, as are health and social care sectors. Housing prices don't appear to be getting better. For this reason I have also thought it is best to only have one, maybe 2 children that way you can focus all your attention and efforts in providing them a good chance in the world with financial assistance.
Ultimately life will get harder, I dont necessarily think in the next few generations it will get so hard that the vast majority would wish they weren't born, but I think it's best to be prepared that life may get harder so you can plan for it (e.g start being more resourceful, gear towards careers that will be needed in future, save up, teach resilience)
Another way I see it is if now suddenly someone told me I was never allowed to eat meat, my food would could only come from UK, you are never allowed foreign travel again, you have limits on fuel to use, and towns are going to get more crowded as people are moving away from coastal areas. Would I still want to be alive and still find joy in life? Yes
In summary, i think things will get hard but not so bad that life isnt worth living, but hard enough that you need to plan ahead and think hard about the number of people you bring in to the world and how you can protect them.