No. You shouldn’t do that. Several reasons.
Residency generally requires an intent to reside, actions to that end and a time requirement. The state you’re “moving” to may have other requirements. Check with the state.
A real address is usually required to get things like a drivers license, voter registration and other proof-of-residence documentation.
You want that proof of residence because, sooner or later, a state will come for you demanding back taxes or proof of alternate residency. A mailbox rental agreement won’t cut it and you will owe not only the back taxes but all the penalties and interest that goes with it in addition to the lawyer and accountant costs. Small gain now, big loss later.
Look into property in a tax haven state with low property tax. Then look for a cheap single-family unit with few neighbors. Buy it. That’s your new legal residence. You don’t have to actually live there. (Don’t buy a property condemned for meth manufacture. You may get stuck with clean-up costs.) Move every piece of paperwork there i.e. drivers license, car insurance, cell phone bill, credit card address…everything. Open a bank account. Change your Social Security address to there. Pay your property tax. Do what a normal person would do if they moved. Then a year or so later, move to the PI (or where ever). Small loss now, no loss later.
(P.S. Don’t use Alaska or Florida.)