The money and fame is in the PGA. Plain and simple. You think Rory would have a Nike deal on the European tour? Maybe. But no where near the money he's getting here. And how do you know these guys aren't going home during those breaks? I'm guessing most of them do.
I know there's decent reasons they choose to play and live here. But IIRC the Euro tour used to be almost the equal of the PGA Tour, which was kind of the impetus for the whole Ryder Cup rivalry thing. That's basically gone now. These are now mostly full-time PGA Tour players and yearlong American residents I think (not sure about all of them, I know from Twitter that Poulter is, I think some others as well).
Not saying the whole thing is silly or anything, don't get me wrong. Team golf is incredibly fun and I'm glad they still have some Euro pride and can generate a rivalry for this thing, which is definitely a highlight of the golf calendar. I was just making a joke. Seemed kinda funny that all these guys are chartering flights from their homes in America to Europe to go take on the Americans. And then someone drew the parallel with soccer so I gave the reasons why I think it's a different situation.