[beeboop]

This isn't entirely accurate. We will not be able to visit the vast majority of the universe even given infinite time if we are not able to travel faster than light. Like 94% of the universe is unreachable without FTL, even without time constraints.

https://www.forbes.com/sites/startswithabang/2016/05/12/the-...

And at some point we also don't have infinite time - we will have heat death of the universe at some point too.

[TheCoelacanth]

The remaining 6% is still orders of magnitude larger than would be involved in a typical space opera.

[beeboop]

I've never actually looked up what the "quadrants" are in Star Trek. Apparently just our one galaxy divided into four. 6% of the universe is indeed an unfathomably large amount of space.