It's true that things are difficult if you don't have primary residency somewhere, but I'm unaware of any obligation to actually stay at the primary residence, so long as you're not de facto residing somewhere else and avoiding legal residency there for tax evasion purposes. Like, you can have a primary residence in NY state, and travel all year long, and so long as you're not actually spending >6 months at a specific residence in another state, and are still paying your NY and federal taxes, I don't think there's any problem. Where things get sketchy is if you're trying to claim NY is your primary residence while living in CA for 9 months of the year. I'm not a lawyer though.
What I'm more familiar with is overseas residency and federal taxes. There are benefits to establishing legal residency outside the US, if you really do live and work outside the US. But then you have to be able to prove it to the IRS. If you can establish a bona fide overseas residency, you get substantial federal tax discounts (like ~$100k tax-free income), and don't have to pay state tax anywhere. But if you spend more than 33 days per year in the US, the burden of proof for establishing a bona fide foreign residency are higher[1].
Edit: update since I can't nest any more replies (to @dragonwriter) below: I sorta changed topics; my paragraph above about foreign residency is only relevant if you're earning foreign income. If you're a US citizen working for a US company, you're not getting away from taxes that way. But you can still save yourself from some personal obligation by setting up a company.
[1]: https://www.irs.gov/individuals/international-taxpayers/fore...