I don't find it embarrassing that they are playing for Wales. I find it embarrassing that Wales are aggressively amping up their 'exiles' program and are openly saying so.
Instead of investing in a program essentially designed to benefit from years of development work other nations have put in (mostly England in this case), why not actually invest in a better Welsh system? Welsh players should not be looking for a development holiday at places like Hartpury if they intend to play for Wales and IMO it's a very poor advert for Welsh rugby.
Re. Tompkins, I'm pretty sure I read an article where he said that he had no idea he was eligible for Wales until they contacted him. I don't blame him for accepting the call up given there had been no obvious interest from England, but let's not pretend he had ever identified with being Welsh. He clearly hadn't.
I rarely agree with Living Sacrifice, but I think I'd feel very conflicted about representing another country I have no genuine connection to, even if I did qualify through a grandparent etc.