If you are seriously arguing that Barcelona were not the most influential team in recent years since the Milan teams of the '90s, I am not sure there is much to talk about. Whether you like it or not, they have become the reference point, to a fault, one might add. Even the manager of the back to back CL winners was talking about how they need to pass and control possession better so they can play that way even against the likes of Barcelona. When the manager of the back to back CL winners still uses that as the level they need to reach, you understand the influence of Barcelona in that period. I think you are simply using a very narrow definition of style. Nobody claimed that everybody is following their specific tactics because nobody can really, no two teams ever play the same. It is the concept that you can win and play on the front foot no matter where and when that became the new standard. Even Pep's teams do not do that the same style, Barcelona, Bayern and City now adhere to the same mentality but the tactics are different.
You claim that it's not about the tactics but more-so about the mentality. You then claim Zidane claiming his team needs to control posession better is him trying to emulate Pep's Barcelona? Okay then. Didn't realise a key fundamental of the game was directly correlated with Pep. Not to add that completely contradicts your earlier point, but okay. I guess when we dominate posession against the small teams, we are also trying to emulate Pep? Feck, must be a feckton of clubs trying to emulate Pep. Bigger clubs (for the most part) are almost always going to dominate or look to find ways to dominate inferior clubs. That's how it's always been and how it always will be, it didn't come to be because of Pep. Clubs weren't oblivious to asserting their dominance before the genius of Pep. That Barca team were able to dominate all other clubs just for that reason - they were better than them. He had 3 players who are amongst the best of their generation coming to their peak and he implement a style for them to flourish. All credit goes to him for that - but let's not pretend he's the father of football because of that, shall we.
For arguments sake let's ignore your contradiction and talk about you claiming "it's about playing on the front foot". That notion didn't come to be because of Pep's Barcelona. They were influential, of course, they were an incredible team, but they weren't the reason for clubs dominating games. Teams were dominating football for long before Pep's bald head reared itself, albeit in different ways of course, which I will touch up on now.
For all this talk of influence etc. it's interesting to see teams over the past few years opting to stray away from that style. Juventus have been very successful being happy to concede posession and play on the counter (doing so and getting the better of a Barca team who dominated posession only a year ago). Bayern won the treble by absolutely dominating Barcelona (who were playing a possession style) due to their sheer strength, pace and power. Madrid have won two CL finals playing a more direct style, happy to concede posession and implement more risk into their style than that conventional Barca side. Just as with Atleti, who have made two finals, beating 'Pep' style teams - both Barca and Pep's own Bayern with defensive, counter-attacking football. Barca themselves have gone away from that style and were adopting a more counter-attacking style with Neymar etc. instead opting for faster transitions.
To claim that style is what all other clubs aspire to - yet completely ignore the fact that clubs have been getting the better of both him and his tactics since his Barca days is what is being narrow, not my views on the whole ordeal.
To claim that Barca team is the template for all other clubs - yet no clubs seem to be trying to go down that route is quite comical. Funnily enough, it seems not even Pep seems to agree with you, as you've stated, even he is adapting his tactics. The fact that he's been getting dished absolute thrashings in Europe over the past few years is proof enough that even though he deserves incredible credit for that Barca team, the players are just as if not even more responsible. They continued to dominate long after he was gone and that was purely down to the genius of Messi.
In fact the one thing you claim is the template for other clubs - is the one weakness I see with Pep. His arrogance. He doesn't adapt as he's too enveloped in his ideals. It's why he's came up short in Europe as of late.
All top managers are evolving the sport, adding to it. Whether or not you believe Pep has been the most influential isn't the discussion. Claiming it's a template for all clubs is where you're wrong. Clubs will always have their own ideals, styles that are synonymous to them. No matter how many Pep's get bred and introduced, there will always be clubs who dominate and win things their own way.
What clubs aspire to do is win trophies. It generates revenue and builds interest. Great football and playing on the front foot helps, but winning trophies is what brings in the money. That's the template all club's follow. That's also the template for most managers. Some of the most successful managers in footballing history haven't always relied on 'playing on the front foot' as they've recognised that. Our very own SAF being a great example of that. He turned us into the juggernaut we are today by implementing his own ideals into the club. He'd play great, swashbuckling football, but he'd also adapt and make things tight if he saw the need to.