The copy of Mathematica I use I get through work. Upgrading this copy is always I time-consuming, pointless chore. I think all of it could be automated. Which makes me wonder:
Is there any way to upgrade (at least from one minor version number to the next) directly from the Mathematica front end?
No, not possible at this time.
While certain parts of the functionality can be upgraded by downloading paclet updates, a new version will contain changes to the kernel and frontend binaries, libraries and other system resources. The best way to upgrade is to run the installer.
Another approach, if the newer version is already installed somewhere, could be to use a tool like rsync to only copy over the modified files into the layout.