Without wanting to engage in all the political rubbish on both sides, it will indeed be interesting to see just exactly what happens to regulation post-EU membership (hate using the term "Brexit" - daft portmanteau made up by some clever-clogs trendy media type) and what happens to EASA.
Things have indeed stabilised, and some sanity has prevailed in recent years. In some cases. Others not.
My own opinion - and that's all it is, just an opinion, so feel free to disagree - is that the damage was done long ago when all this nonsense started with the JAA which grew into EASA. I'd rather be done with it to be honest.
If the CAA need to "start again", that's their problem to sort out. The CAPs would still exist and any existing EU legislation would be ported across to the CAA. Charges are still levied by and paid to the CAA so all that would happen would be no money going to EASA...
...but of course nobody really knows the truth. Happy to be corrected for anything I've said that's wrong.