[jaydaigle]

I'd agree with this entirely, honestly. (Including the sleight-of-hand I'm engaging in to make things seem exactly the right amount of weird; see footnote 14.)

Infinity is so weird that it's really hard to agree on what infinity "should" look like. And the axiom of choice only matters in situations where the weirdness of infinity really kicks in.

So yeah, some people look at the whole list of AoC equivalents and think they all seem pretty reasonable. And other people look at the list and think none of them seem that plausible. And a lot of us are split, and find some of the claims obviously true and others obviously false.

One of my goals in this piece was to try to let everyone see both sides of this: why you might find the axiom compelling and why you might find it troubling. And then to offer a pragmatic resolution at the end, which is basically another take on what you just said.