Using states as laboratories is one thing, but using them as laborartories for Socialism is another.
What if a governor decided to experiment with a system of taxation and wealth redistribution, that would result in every resident of that state ending up with exactly the same after tax income? Would the “laboratory” concept justify that?
Based on the Founding Fathers’ vision, a state is pretty much free to do what it likes. The Constitution does set limits, you can read about those specific limits in Article I, Section 10...and of course the various amendments apply.
As to your specific question, the constitutionality of “equal protection under the law” in Amendment 14 would make it somewhat difficult to enforce the type of law you describe. (Although “progressive taxation” in my opinion is a form of wealth re-distribution, and sadly many states have instituted that!)
I submit that even IF a governor/legislature of a particular state were to succeed all challenges to such a law, there would be a mass exodus of PRODUCERS from the state—and the states economy would collapse. You’re seeing that in California now. While they don’t have exactly what you described, the increasing regulations and onerous taxes are causing people to flee California.
I think Wisconsin at one time (or still today?) had a school voucher program for parents of failing schools. Worked wonders—and other states tried or are trying to imitate it...of course the liberals challenge it in the courts everytime it is attempted...but I think you get my point: a state ought to be free to attempt to meet the needs of its own citizens. What might work in Maine may not work in Utah. :)