This should be where we stand going into 2021 redistricting, assuming this decision also gets applied to the NC congressional districts. Green = significant restrictions on legislature, Yellow = completely independent process
Notes:
CT+ME: 2/3rds of legislature needed to pass a map
OH: partisan maps expire after 4 years instead of 10
KY: state constitution prohibits splitting counties unnecessarily (so cannot gerrymander KY-03)
NY+UT: commission proposes map that legislature can amend within certain limits
You've correctly noted the restrictions in Ohio, but I would not deem them significant.
Are they really not? I thought the restrictions on city/county splits was a rather significant one. In other words, for example, there should have to be a district entirely within Hamilton County that contains all of Cincinnati.