I recognize this is just my personal experience, but this doesn't hold true for me in the slightest. I grew up and lived in CA for over two decades, but now located in a state with no income tax and employed by a company in the bay area. I pay zero state income tax, as do all my coworkers in the area.
Which is often just not that necessary... must people's income levels in retirement are low enough that CA's income taxes are competitive with many other lower-tax states (not those with no income tax, though, of course).