But yeah, full Wayland desktop (well, sway) and Firefox -- no problem. I occasionally use a debian chroot to pull up gnucash (accounting program) which works as a backup but it's rare. My debian chroot is mostly to run a 10 year old printer driver from Epson that's compiled against glibc, but doing a little trickery with a small C program works just fine with CUPS still running in alpine (print filters operate on stdin and stdout, so you can launch them in a chroot by themselves no problem).
Not so much, actually. When you aim for anything that resembles modern “desktop computing” (maybe with at least some “web browsing”), you are limited to decent hardware configurations from last 15 years or so. Yes, you can show to your grand-grand-grandkids how it really was back in the days once, but you are not going to study the splash screens while programs initialize, or wait for each image to appear for a couple of seconds when skimming trough an archive, or watch page load progress bars move in the browser. But with that decent hardware, you almost always can install bog standard modern Debian with an ascetic desktop, and have much less support issues than with specialized system. It'll be the same Linux anyway.
Although it is possible that it won't work for some top performance purely 32 bit CPUs, because non 64 bit builds are certainly out of fashion today, even though some 32 bit distributions still exist.
LFS has the topic of package management covered quite nicely I think[1]. They describe the contraints and approaches that might be possible, and what the real world solutions to those are (PRM, DEB, et al).
There have even been some package managers designed (or at least discussions of what the design would look like) for LFS explicitly over the years, but none seemed to have come to fruition, and I can't find any links to them.
1: https://www.linuxfromscratch.org/lfs/view/9.0-systemd/chapte...
Edit: found the announcement https://www.gentoo.org/news/2023/12/29/Gentoo-binary.html