Should there be a United Kingdom team instead of teams from each country in the UK?

New American Football fan here, so please be gentle. Especially because I’m probably about to suggest something sacrilegious/ heresy . But, is there a reason the UK does not play as a UK team instead of as England/Scotland/ etc.? It would seem, just by pulling from a bigger pool of players, a combined side would make a stronger team. Do folks from Wales and Scotland prefer to have their own teams, which will struggle due to their smaller populations as opposed to having a few players on a more successful UK side? Would English fans want the added talent or prefer to stand on their own? Has this idea ever been seriously pursued?