update-initramfs very slow
I had this problem, and booting was also very slow (on an older machine). It had to do with compression and the method having changed from gzip to bz.
I eliminated compression altogether by using COMPRESS="cat" in /etc/initramfs-tools/initramfs.conf and now both building and booting are super fast. (The file name and directory can vary by distro and distro version.)
This fills up more of my /boot directory but it wasn't close to capacity in any case.