High earners benefit from no tax states because they can make as much as they want without paying more taxes. This may offset higher tax in other areas when the income is significantly higher.
You'll do well in a no tax state if you don't go out and spend tons of money. States like Tennessee have a sales tax up to 7% that can be seen as more costly than Washington state where there's 0 sales tax.
Since tax builds revenue for the state, the state will get their money one way or the other. You're more likely to benefit from living in a no income tax state if you don't own property.
You may not find lots of public services in a state or area that doesn't have high taxes. If you need these services, you might need to pay the taxes for it.
If you're trying to save money to invest more money, a no income tax state can help. But it will require you to have solid income and live a little frugal to maximize the return.