It could be as simple as you say, but the problem is the EU is very good at protecting it's internal market. Having mutual recognition of of a third country, that while currently aligned may diverge from EASA rules, over whom they have no control, who doesn't pay in to their budget and who won't accept rulings of the ECJ. Don't think they believe they have a choice.
With the current crisis and many EU pilots losing their jobs. They will protect EU pilots from competition by British pilots.