Which states would this qualify for?
From my limited knowledge:
Most powerful:
New Jersey's has the power to appoint all state row offices, something I don't think that exists in any other state, which is immensely powerful, especially appointing the Attorney General. Maryland's has quite a bit of power over the budget even with an opposed legislature, which is why Hogan has managed to get more done than you'd think with a veto-proof opposing majority. Florida's apparently has the ability to dismiss and replace county office holders, which is pretty significant. Any others?
Least powerful:
The Governor of Texas can't even appoint the State Supreme Court or issue pardons unless they're first recommended by a state agency on pardons. For such a large and important state, it's a shockingly weak office and mostly ceremonial. The Governor of West Virginia has a very weak veto power (only takes a majority vote to override unless it's a budget bill), and seemingly mostly just ceremonial duties. Their only serious power seems to be the ability to call a special session of the legislature and have budget vetoes upheld. Any others?
That's actually a pretty good idea, and I'd support something similar being implemented at the federal level to prevent presidents from abusing the power to pardon.
Look up the case of Benjamin Spencer. It's making freeing him much more difficult.