I dunno about Welsh/NI people, but as a Scot I'd struggle to get behind a team GB with 0 Scots playing
That decision exists only as the our football organisations made the divisions a very long time ago. Impossible to change now.
You could almost say if I'm from x county and that if there are no x player in the team from my county, I won't support the national team.
I'm very happy to support athletes in the Olympics and other sports no matter where they come in the UK.
On another topic, Scotland for the last 20 years has been shockingly under performing in the quality of the players they produce in both Football and Rugby. There statistically should be more chance of Scottish players getting into a UK Team than Welsh.