There are a couple pieces to that, not the least of which is Canonical wanting to push their new 'snap' format, for better or worse. The other thing is that Apt is not a good fit for the task - say it's daemonized programs instead of live patches. Apt only takes responsibility for downloading the bits onto the machine and unpacking them, and init/systemd is responsible for actually running programs.
However, for live patches, it's critical the program be running/the patch installed, and Apt doesn't manage running processes, nor does it have a UI whos purpose is to report on patches that have successfully downloaded but fail to install. These aren't fatal problems, but those aren't features upstream apt is likely to want (maybe systemd wants to swallow apt), so then you're forking apt, with all the work that entails. Might as well just write your own thing in that case.
But APT does. It can run the post-install script for the package, which can certainly include the live-patching bits. It's not like live-patching needs a continuously running daemon.
Saying that APT can't do this is nearly equivalent to saying that APT should not be trusted to run any post-install scripts at all, which basically means it shouldn't be trusted to install half the software out there.
However, for live patches, it's critical the program be running/the patch installed, and Apt doesn't manage running processes, nor does it have a UI whos purpose is to report on patches that have successfully downloaded but fail to install. These aren't fatal problems, but those aren't features upstream apt is likely to want (maybe systemd wants to swallow apt), so then you're forking apt, with all the work that entails. Might as well just write your own thing in that case.