> what are the applications for custom ROMs on DSs and other handheld systems?
Having played around a bit with a jailbroken Switch, the primary reason is to be able to either run mods for games (e.g. there's a surprisingly viable set of tools for converting/bundling Skyrim mods for PC for use on the Switch version) or to run homebrew apps, the common ones being emulators. Previously, I had played around with GBA emulators on PSP/PS Vita, but the Switch form factor and screen size are a lot nicer to play on.
That being said, you could also go the route of putting a completely foreign OS instead of just modified Switch firmware. Android seems to run flawlessly on a Switch from my testing; even though Android doesn't seem to be able to access the joy cons directly when they're attached, you can still pair them with bluetooth and they work fine even when they're slotted in. Android even seems to have pretty good built-in support for that kind of input device; you can easily navigate through the icons on the home screen, hit "A" to select whatever's highlighted, etc.