But you can just take sporadic matches between sides that especially don't see each other all too often into great account. The European teams discussed on this page just have more quality and more top level depth.
Take Portugal for example who probably rank somewhere just below the true euro heavies and their record at European championships since the turn of the century.
2000- semifinal
2004- final
2008- quarterfinal
2012- semifinal
2016- champion
I don't think many would suggest the USMNT would achieve those type of consistent top tournament finishes let alone qualify for every tournament if having to do so those UEFA.
Portugal is a really bad example of a European team that the United States should be completely overwhelmed and worried by. Especially since you reached back with the dates.
The US has played Portugal in two major tournaments in that time frame being in their group. They beat Figo and the boys and were unlucky to draw with them in Brazil. Both times they advanced out of the group ahead of Portugal.
A team that could go that deep in the tournament suggests if the USA was qualifying for the Euro at some point they would have likely had some encouraging results.
Honestly I would love if the USA was allowed to exit their region and play in European qualifying (like Australia leaving Oceania for Asia) I think it would elevate their performance seeing better team more regularly. That or a consolidation of the Conmebol and Concacaf regions.
Greece and Portugal are not world beaters and they have managed to win the Euros. It is not hard to believe that the US could have a big tournament and that they would still likely represent top two in their group in World Cup Qualifying. Yes they would risk more in terms of needing a good draw at times or the right playoff matchup. It also sort of ignores the idea that in a two leg playoff that Columbus, Seattle or Kansas City would be easy dates for whatever European team. They have a substantial record at those places when the chips are down and qualifiers aren't really the same either when evaluating how exactly you think Ireland, Portugal or Switzerland is likely to fair in that playoff format as well.