I haven't really downplayed them. I think it was a brilliant side, player for player the best the Premier League ever seen.
I don't necessarily disagree that Premier League's four best teams was maybe four of the five best teams in Europe, but that tells you much more about other top teams in Europe that year rather than the Premier League. Just look at it: Juventus was recently relegated, Milan was on a downward spiral, Inter was good, Madrid was right in the middle of six R16 exits, Barcelona was good but in the end of an era with Rijkaard, PSG wasn't really at all and Bayern wasn't even in the CL. I know a lot of people downplay the success had in Europe by English teams in the past years because top teams in Europe aren't that great right now, but in reality the top teams in Europe has never really been worse than at that time.
As for looking out of place, they probably wouldn't. But we needed to park the bus in order to get by (a not great) Barcelona-side. We were a great side indeed, but the reality is that there's happened a lot in football during the past 15 years. This happens in every sport really, the general level increases over time. Take Mourinho as a prime example, the way his teams play clearly worked a lot better 15 years ago than what it does now. It's not that he's not good at doing that anymore, it's that football has evolved from those times. It's not that we didn't have talent, but we didn't really impose ourselves in the same way as top teams do today, and because of that I think we would have had a hard time truly keeping up.
If we had that exact team today, SAF was 15 years younger, he'd most likely have applied what we today call a modern way of playing, then we would obviously have been one of the very best teams in the world, and probably the best right now. But if the hypothetical scenario is taking that exact team playing the way it did back then and putting it in todays football, then yes, I think it would have struggled. It does not make that team any less great, it does not make SAF any less great, it's just a reflection of how sports evolve over time.