In general, I'm inclined to think that in a democracy, the people should have more direct influence to things “closer” to them (by some measure), and less for bigger, nationwide, issues, of which they presumably have less understanding. This is, in fact, how most democratic nations work in practice.
The case of Boaty McBoatface, though, is unusual in that it doesn't actually much matter what the name of a research vessel is. It's just a name. Names are almost always boring. Unless… if the name becomes so popular and widely known that the very name opens up completely new opportunities for raising funds and awareness. Which, I would have thought, was kind of the point of the competition to begin with.
So, why not reap the PR benefits of this name? Why would they start a contest but back out when they hit the jackpot? I do not understand.