Yes. It is done this way on EPEL distributions (i.e. Fedora, CentOS, Scientific Linux) and Ubuntu. However, it is not presently done on Debian and Gentoo. I am hopeful that this will change on Debian in the future. Gentoo makes kernel upgrades the responsibility of the system administrator, so this does not really apply to it.

WRT to Gentoo, Gentoo does have a tool called genkernel that I consider to make such upgrades fairly easy. It can handle any of initramfs generation, kernel compilation, kernel configuration and bootloader configuration (GRUB2). However, it does have a moderate learning curve. I am also one of the genkernel developers, so I likely have an implicit advantage over users in understanding genkernel. In particular, I find some users have difficulty discovering its functionality, despite it having things fairly well documented in the man page. There is likely more that needs to be done in this area.

That's exactly how it is set up. Just install a couple deb files or set up the repo and DKMS does the rest on every distro I've tried it on.