You can get custom songs on Quest, I have probably 99% of my Beat Saber play time on them, search for BMBF on google.
Most of my custom songs on the Quest I've done have actually been for the game Ragnarock, because it doesn't require sideloading anything, just copying files onto your Quest from your computer. That one is quite fun also.
It does give extra peace of mind having the games run locally on the device in case of connection issues, and to avoid the occasional need to run upstairs to fix something.