The lightcage (limit of speed of light travel) will kick in faster than you would expect. I believe it is less than 1000 years at current growth rates. It's like compound interest.
I'm not saying we will destroy ourselves, I'm just saying given how unfathomably large space is, that even if we could travel at the speed of light... We'd be going nowhere.
Even if we never find a way around the speed of light limitation, and even if we never figure out how to terraform planets, the amount of resources in our solar system is vast and there's still a great opportunity for expansion with O'Neill colonies.
Obviously that requires very futuristic tech and will not be happening for a very, very long time. Still, it's worth working towards because I believe expansion and exploration is in our DNA. We just need to know when we've hit our limit for a given environment and not live beyond our means.