I'm guessing one of the reasons EASA at least wouldn't want to recognise UK CAA licences is that through Brexit, a big market for EU/EEC pilots has been closed off.
The requirement to speak English to a reasonable extent in commercial aviation meant that anyone from Europe could fly in the UK whereas anyone from the UK would have needed to meet national language requirements to fly for many (but not all) EU/EEC airlines.
On the flip side, the inability to recruit large numbers of Europeans has possibly been one of the factors in UK airlines starting to take fully sponsored training programmes seriously.
I'm going down the dual-licence route (eligible for Irish citizenship through ancestry) and some of the bureaucracy has been a pain, especially since fewer and fewer UK commercial flying schools offer the dual-licence route and the fact that AustroControl apparently won't even accept UK night ratings, however it is possibly a price worth paying for less competition in the UK low-hours jobs market.