There are three things you need to remember as a starship captain: 1) keep your shirt tucked in; 2) go down with the ship; and 3) detailed knowledge of ornithology.
Halley is the one who predicted its return mathematically. I'd say that's more significant than seeing it twice in one lifetime and supposing that it's the same comet.
Unpopular opinion: Considering the fully automated luxury space communism Bashir has spent his whole life in, this is actually an incredibly tone-deaf thing for him to say. (Which is in character for early-seasons' Bashir, TBH. c.f. his introduction to Kira in the pilot.)
The writers intended a moral objection to preventable human suffering, but actually wrote the 24th century equivalent of "let them eat cake".
The true captain will give up the chair rather than see it cut in half.