I’m self taught, and I tend to think of flats because I tend to downtune. I think others choose the flat or sharp based on their desired key. That doesn’t help me describing a tuning if I’m playing out of the tuning’s assumed key! I have adopted one set of tunings which requires bringing the second string higher than the first, which I usually dedicate to a guitar with the strings swapped so I don’t break them all the time. (Adapted from very closely watching performances by Kelli Rudick if you’re curious.) I always describe the 2nd string tuning with sharps unless I have a good reason not to.

None of this is meant as advice, it’s just how I reason about using the instrument myself in ways it wasn’t necessarily intended.

I assume it's because tuning a string up can break it, while tuning it down is harmless.

I would guess that it's to do with the fact that musicians generally use the key with fewer sharps/flats. E.g., Bb major (2 flats) instead of A# major (5 sharps). This also follows what's on the circle of fifths, where major keys clockwise from C use sharps, and vice versa.

In the case of drop Db, I would also guess that people just think of it as "slightly lower than drop D", hence just adding a flat symbol.

Nit pick: A# major would be 10 sharps, at least written following the usual convention of each note letter being used exactly once: A# B# C## D# E# F## G##.

What is 2 but 1 plus 1? The key of B flat is easier to read.

Disregarding how it'd be read, I suppose you could theoretically get into keys like G-triple-sharp or F-quadruple-flat -- but that's just overcomplicating things, isn't it?

I really don't know why that's the convention. I always assumed it was due to the minor scale/modes having so many flats. The only mode with a sharp is Lydian - and that's a single sharp! Even the major mode Mixolydian has a flat! Natural minor has 3 flats.