I think the likely course of technological development seen from today would be contrary to the ethos of Star Trek. For example, I think interstellar exploration will almost certainly be conducted almost solely by automated probes, and would be the far better done because of it. I think modern neural and computer science increasingly point to the fact that human have nothing unique that can not be surpassed by machines, so the omni-emphasis of Star Trek on "command decision" and "human intuition" is itself an anachronism.
Or, perhaps like the TNG "Interface" probe, space exploration would be done virtually with the probe being guided/interfaced by a living human who could be light-years away. This would eliminate the need for starships, starbases and a space armada. (Though it would not sidestep the notion of human colonization of distant star systems, would it?)
No, if humans want to live in moderate comfort for several thousand years more, they would need to colonize. But except in setting grand strategy, their decision making or presence, tele or otherwise, would be increasingly superfluous and harmful towards attainment of tactical objectives.
There might still be a need for an armada, so long as there might be civil war amongst humans or possible hostile aliens. but it would likely be almost totally automated and AI controlled, with human input at grand strategic level at most, plus a safety kill switch.