Looking back it's a strong but unbalanced squad that was always going to be tricky to make an elite unit out of. 4-4-2 didn't suit Gerrard or Lampard, and 4-3-3 didn't suit Beckham or Owen. Rooney was patently unfit and in the documentary he even says he shouldn't have gone. When you try to build an XI it either looks tactically shambolic, includes a few average players like Crouch or Lennon in place of much better talents, or both. A solid defensive team that hopes to win games through flashes of individual quality is what they were and I don't think they could ever have been anything more.
The tendency at the time was to dismiss cohesion problems and say things like "you just pick your best players, they're world-class and they should be able to figure it out". This in turn led to a lack of respect for B-tier nations, because pundits were unwilling to accept that a well-organized unit could compete with a team of stars. Ecuador had beaten Brazil and Argentina in qualifying, but the English media treated them like a speed bump because they hadn't heard of any of their players.
There'll always be some jingoism and a tendency to overrate your own country's prospects is all part of the fun. What stands out relative to other tournaments is the negativity that followed victories in 2006. In the documentary, Rooney describes feeling elated coming off the pitch after scraping wins against teams that pushed them all the way, only to discover that the national media response was one of frustration and anger at how difficult those games had been. And I do think that's changed. Euro 2024 might be a better example than 2018, because they really were worse than they should have been, but the country didn't think it was too good to unreservedly celebrate a scrappy win over Switzerland.