You are wrong. Many teams have a blueprint of the type of team that they want to be, which gives them an identity. It’s been that way forever and it will always be a thing. Some teams are smashmouth, run it down your throat. Some teams like to pass to set up the run. What was our identity?
You are missing the point, find me a smash mouth team that can’t block. Passing to set up the run sounds great, find me a team that can’t pass block that is carving out their place in the league with that identity.
Teams certainly want to do things, but without the right pieces they won’t get done. And announcers will have the cliches of “team X is just trying to find their way” or “team Y is trying to get back on track”.
Strategy is a choice, so-called identity is the result.