Can someone explain why I'd use snap or flatpak over the distros repo or manual install for something not in the repo or unavailable via adding a repo? Apart from auto-managed updates. Snap and flatpak are massive compared to "traditional" packages.
Also updating the system shouldn't accidentally break the application you use either. On rolling release distros this can be a pain. You'd typically want the application that the application developer tested properly (as opposed to relying on your package manager's "testing"). The packagers can introduce bugs while repackaging an application for X distro. My Cura was broken for so long on Arch linux that i gave up and started using their AppImages instead.
Depending on your distro, you also have to deal with headaches like XYZ software is only available on Ubuntu 20.04. Tough luck that you are running 18.04 on your laptops. (last week i had to deal with this problem with clang)
In addition to being self contained with all the dependencies, these solutions offer some level of sandboxing too.
On Arch, AUR usually does a nice job of packaging binary only applications, so i rarely need to use flatpack/snap/appimages but on other distros that can be a pain.