UKGov don't know whether Brits have dual citizenship until you apply to renew your British passport & now have to send scans of your non British passport. Of course many EU citizens don't bother with an EU passport as they can travel within Schengen on their IDs anyway!

I agree with your premise but just want to say that 4 of our family emigrated to EU while we could pre Jan 2021 specifically due to Farage's Brexit.