If you live in California, you likely have to register in California. So you really only have one option, unless you want to register in two places. You’ll also have to pay at least $800/year for the pleasure.
The follow-up question then is... what are the legal workarounds to avoid having to also register it in one's home state, e.g. California? Surely there are some.
This is kind of California specific. There isn’t really a work around if you’re “doing business” in California.
Does this imply that any business that's not registered in California can't do business in California?
Um, it implies that if you’re “doing business” in California, you are required to register there? “Doing business” has a specific definition, any single member LLC where that member lives in California qualifies.