You don't need an LLC to run a business. Plenty of sole proprietors do this along with filing self employment taxes without ever forming an LLC.
Does something prevent incorporating in another location that allows it? Doubt it.
Of course they could do that, but any corporation or LLC that does business in California [1] (surely a Uber driver operating in California would be considered as such) has to pay the fee. Incorporating out of state would just mean a second set of fees and more forms to file.