Some say that the fact that the EPL is a top league has little to do with English players. I not sure about that, but it is certainly true that the national team as a whole appears to be lesser than the sum of its parts.
Yeah, I wouldn't go that far either, and for example, not many of the top English players play in foreign leagues. Almost all of them are in the EPL, so that's the kind of game they know. Having followed Inter for the last couple years, it occurs to me that the Italian game (as annoying as it can be) is much closer to the style of international soccer than the EPL is. The more conservative, sit-on-a-lead, dive-in-the-hope-for-penalty-shots style they play is more similar to that of the World Cup. This is another parallel with US basketball: the NBA players are used to one-on-one acrobatics and flashy plays, while the international game depends much more on passing and positioning, skills that many US players have neglected in search of NBA riches.
The US national team often struggles with the fact that it is often composed of MLS all-stars rather than all of the Americans playing in Europe, when the latter are our best players. This seems to be a combination of scheduling conflicts and the fact that US Soccer is trying to promote the MLS.
MLS has been struggling with that balance since its inception. On the one hand, to grow the league you need some of the top U.S. players scattered around the major markets. But unless the top players play against the better competition in Europe, it's harder for them to rise above their domestic level. (Or even for coaches to know who deserves to be on the national team!)*** Is Landon Donovan better served being a bench player in the Bundesliga (which he was) or a star in MLS? You can see both sides of it.
There are two other issues:
(1) CONCACAF is just not a very competitive soccer region. The U.S. and Mexico have a lock on two World Cup spots, while Canada, Costa Rica, and a few others fight for the third. Sure, they don't schedule nearly enough friendlies against European and South American teams, but they also have to play often against weaker competition too, at least compared to Europe. European teams have to run a gauntlet to qualify for Euro 2008 or the WC every time.
(2) The MLS season spans spring to fall, instead of fall to spring like the rest of the world. That makes scheduling harder and really complicates the logistics of the national team. I'm not sure that syncing the MLS with Europe would help that much though. It would mean competing more with basketball as a winter sport. And harsh northeastern and midwestern winters would hurt the quality of play and attendance, since places like Chicago, NYC, and Boston have far colder winter weather than anywhere in England or France.
*** This, by the way, is why I think most of the U.S. players that have made it in Europe have been goalkeepers. It's easier to evaluate a keeper's abilities (positioning, reflexes, etc.) against inferior competition and get an idea of how he will do in Europe. But trying to predict how an MLS defender would do in the EPL is much harder.