people prefer AUR over Flatpaks. Why?

Some stuff doesn't work as Flatpak, or I actually prefer for it to be compiled against what's actually on my system rather than a generic one-size-fits-all binary, or simply isn't in Flatpak.

Flathub is tiny (under 3k packages), AUR has over 85k – and yes I know that many of those are abandoned or maintained very loosely but even if you only count the packages updated in the last year that's still over 10x bigger than Flathub.

Examples: kernel modules, CLI tools, libraries, versions of apps compiled against old UI frameworks (like Claws-Mail with GTK2), obscure apps, drivers for obscure hardware, stuff with dubious legal standing like file sharing apps etc.

how do y'all cope with waiting for all the AUR installed packages to rebuild after every update?

I don't. I disabled AUR updates and only update AUR packages when they break. Sometimes if I'm bored I'll run a pamac checkupdates --aur and do a pamac build <package> on anything I see there that might be interesting to have a new version of. But most of the time like I said I wait for them to break, which happens surprisingly seldom.

Alacritty takes ages to build for me.

Yeah some apps are ridiculous. Pika Backup is another example, RPCS3, and so on. For some of those I actually resort to Flatpak.

The choice is not always so clear cut because Flatpak stuff will tend to have random features present or missing. For example a while ago the Flatpak Handbrake could do accelerated encoding on the GPU, now it can't. So I was forced to go back to native Handbrake.