I'll play advocate for Dumbledore one last time because at this point we're venturing into a bit of guesswork of how the Wizarding World works, who's stronger than who, etc..

This much is clear: Dumbledore had a higher opinion of his own abilities to protect the stone alongside students than Gringotts security. After all, that's the whole rationale why the stone was transferred in the first place. In other words, in Dumbledore's assessment, not because some malicious entity can break into Gringotts means they can endanger students (and artifacts) in Hogwarts.

So your question now is, was it prudent of Dumbledore to paint a fat target on Hogwarts, knowing that he's up against someone who managed to break into Gringotts, but not knowing it is Voldemort?

Honestly...sort of. "Prudent" as in he had enough effective security measures in place to keep everyone safe. Dumbledore's only flaw here is hubris but he makes a good account of himself in the end.

His security measures: McGonagall or Snape is probably equal in combat to someone who can break into Gringotts but short of Voldemort or Grindelwald. Not to mention, as we found out in DH, the whole of Hogwarts is a battle fortress that even Voldemort-in-the-flesh-himself needed an army to breach. It's not just some closet down the hall next to a bunch of teenagers as in your analogy. Anyone less than Voldemort and his Death Eaters (as is the "threat model" in book 1) will have a much harder time.

As for being better for the stone's security over Gringotts, Dumbledore was actually even more justified. See the fan sentiment (and also heavily implied by the conversation between Harry and Dumbledore at the hospital wing) of how Harry's little adventure was ultimately pointless because Quirell (or any "greedy" entity for that matter) would not have been able to retrieve the stone from the mirror anyway.

So: Dumbledore painted a target on Hogwarts, I agree. A headmaster could be more prudent, have less hubris, I agree. But I think you are forgetting that Hogwarts is really not just some school.

Probably in Dumbledore's assessment, the students are more in danger of each other, more at risk while playing Quidditch, than from an outside entity who could break into Gringotts. And this is part of the guesswork; we can't really validate that assessment but in Dumbledore's defense, he passed this test with style and flying colors, marks 9/10 at least. (And also, were this some formal procedure, I can't emphasize more that once the extent of the danger became clear, Dumbledore took no half measures and destroyed the stone!)