You are very incorrect about NH, it lacks income and sales tax but property taxes are extra-high to make up the difference. The same is true in other states that lack income taxes like Texas and Washington.

(It’s particularly bad in Texas because the largest landed estates like ranches use various tricks to avoid paying most property taxes so the regressive burden ends up falling even harder on the middle class, who now has to pay the entire share of funding state services. I don’t know how Texas keeps up this reputation as a low-tax haven for fleeing California, the reality is that you’ll be paying gobs of property taxes unless you’re either a renter with no land or a baron with tons of land who can schmooze your way out.)