I don't think that upgrading the kernel is a good idea, ubuntu does that, and what happens: tons of users that "magically" their systems are unable to boot anymore (or wifi stopped to work), makes no sense to upgrade an already-working kernel "for that machine"
that is also made on purpose, as explained somewhere elive is a rolling-release in the every same way debian it is (and uses the same way), but as we know (already explained on that page), there's some features that cannot be added with a simple upgrade, for example
- newer packages selected to include on the distro
- personal / user's customizations
for the second one, people can use elive-skel at its own risk (we don't want to wipe out the user's personal configurations everytime an improved default one has been updated). Example: 3.7.11 will include an improved cairo-dock with wifi and hotkeys extra icons added
So in short answering this part:
- it is made on purpose that grub shows statically the number on which has been installed (even if user keeps up to date its system with apug or personal configurations), its a nice way to remember the version on which has been installed and optionally, do a new install (upgrade-mode) in the future.
live patching is another thing and if there's really the need to update the kernel due to a security thing, then could be done via elive-upgrader interactively
on such case you should drop it also for debian itself saying that they are not rolling-release, because elive is using exactly the same way debian does