Torrent was doing really well at NYCFC after a tough start. They were looking great before he left, which was due to issues higher up. They were definitely going to have been stronger had he stayed. They 100% tried to play the way Pep does. They played their way through teams with great build up and we're majorly vulnerable on the counter, but they made it work thanks largely to players like Moralez and Heber.
Playing the same way throughout generally tends towards success if the coaching is right. Imagine if in 16/17 Guardiola changed the way we played for a few extra points? We may have achieved much less than we did the following two seasons because we'd have lacked the know-how to play a specific way (like Mourinho sides suffer from).
As with NYCFC at the moment with Delia, the women's team with Taylor, and whatever other team in the CFG (men's, women's, or academy) the philosophy itself isn't the issue, but the implementation. You need good coaches that coach the right kind of way and are actually skilled enough to get the players both playing that way and to motivate the players to make it work. Delia does not manage the "right way" and Taylor is unknown in coaching ability despite having the right ideas.
Having the wrong style of player hurts too, but that's more down to recruitment. And with good coaching and time you can generally get the players to be competent, which works fine in weaker leagues like the women's and MLS.
With regards to identity you NEED to see the bigger picture. Each of these clubs may have its own identity but each of these clubs are part of the CFG. And importantly they are all branded under the CFG brand. So when casual US fan #23453 sees a CFG team on the TV they're expecting to see swashbuckling and great technical football. And that future might not seem obvious now, but if these clubs stick at it for the next 10-20 years, which is how far ahead ADUG are planning almost certainly, then it makes far more sense. If they keep at it for long enough then it will work, and it will be part of these club's identities.
It's a short term sacrifice for an incredibly huge long term gain. You might not think it's the right way to go and that's fair but the CFG has to push these things in this way if it wants the results they desire in the long term furture.