"Giving up" seems like the wrong rubric here because you haven't even identified the goal that putting people into space would accomplish so I can't judge whether or not doing that would actually further anything. Whenever I press people on this it generally comes down to "because it's there", which was also a bad reason to climb Everest.

I can think of three worthwhile goals at a minimum:

1) Access the vast resources available elsewhere in the Solar System.

2) Move most polluting and destructive heavy industry off of Earth (this will take big advances in propulsion technology).

3) Provide good habitats for humans and ideally much of Earth's ecosphere elsewhere in the Solar System. Certainly the human population alone could rise to the hundreds of billions if desired/needed.

Surely it'll take a lot of progress to achieve those goals, but they're within reach of our current scientific knowledge. Interstellar travel, on the other hand, is much more of a stretch goal! ;-)