Would disagree mate, identity is a very real thing in football, you can call it a number of things, culture, values, mentality, method and application. You can call it anything you like philosophy or whatever, its semantics really.
Most teams have a descript identity and you need it for cohesion and clarity.
City have one, Arsenal have one, Spurs have one, Villa have one, Brighton have one and a few others - its a sign of a good manager when you can implement one.
A team that doesn't would be Utd the last few seasons and Chelsea at the moment, prob Palace at the moment also and arguably Forrest. They will talk about transition and maybe that's right - but overall its trying to imbed what i talk about above.
Take our last what - 5 managers each tried to impart their own sense of identity on to the team, Martinez was different to Moyes, Koeman, Sam was different Silva, Carlo was different to Marco, Benitez was different to Lampard, Dyche is different to Lampard.
Its fundamentally important in my opinion, we haven't had it consistently for beards, regardless if you are are fan of it not, we are at a point where we need consistency in identity and build on that for a few years.
I don't disagree with your analysis of how we play, but i think the lack of resources prob dictate what we are capable of offensively. Its a very real thing as we know from the porridge we are in.
Somehow we're competitive.