As someone who coached nearly 25 years against private schools, but now as a parent has kids in a private school it's a touchy subject for me, because I definitely see both sides. That said as a former coach my issues was a little more complex as I was from a relatively rural conference (1A and 2A at the time) and tbh I had a great deal of respect for the local private schools and never felt like I was being recruited against and generally in conference and district play generally always held my own.
The problem I ran into is as a soccer coach where it was primarily only 2 or 3 classes prior to covid when I stepped down, the issue was always the private schools in densely populated/metro areas. Where not having district lines and being from large cities really impacted things. The Xavier's, Assumptions, Reginas, etc... Those were the programs that I totally respected, but at the same time absolutely loathed because they were pulling from 3A and 4A districts and competing in 1A/2A at the time. As stated I was in Southeast Iowa and TBH our local private schools didn't bother me simply because even going a 30-45 minute radius from those schools there simply wasn't that many kids to pull, but that's simply not the case in bigger cities/metro areas. That was the problem I have then and now. So in more rural areas, depending on the sport, I didn't see it as such a huge issue statewide because I think public schools had an advantage, but as you moved closer to the bigger cities that advantage disappeared and you found yourself facing dynasties.