I think the point is that you don't need to be the man with the armband to do any of that. As others have said, Carra wasn't the captain, but he still did most of what you're talking about (Although only from a certain point, he was regarded as a liability for a while) and you could take the armband off Gerrard but he was not going to suddenly go quiet or start playing differently. Fetishising the captaincy isn't the answer, it puts too much on one player. What if he's out? The problem with following leaders is what everyone does when the leader is gone and suddenly they need to think about things they are not used to thinking about. It's better if there is a collective responsibility.
I understand that Nessy- which is why good teams always have 2/3 such players AND then those who choose to learn. You can always increase the mentality of your team naturally BUT only if you have a leader(s) who those who have an affinity/talent for that sort of thing, can look up to, observe and learn from... but if you have a caricature of such a person... well then- you'll have caricatures as their spawn. We'll only have ourselves to blame then.
Also, I agree- you don't need the armband. I was looking at it from the fundamental pov, but what I'm getting at is the same- a leader will rise to the position though- that's just inevitable and the hopefuls will remain his enforcers(ala Carragher). In the absence of the official captain- there's no biggie- one of the others step up easily, they will naturally do that.
But we're not even there yet. I admit- that's an idealistic view, but if we can "half" of that, we'll be a different team.
I get those arguing for "leaders throughout" the pitch and I want that- believe me I do- so what's the next step? How do we improve the situation as soon as possible? We want to see results and we should START to rectify it as soon as possible. When can we realistically do something about it? If you have a squad already- which you built with quite a "bit" of effort, then all you can do is to start recruiting with mentality high on the list, henceforth and hopefully, your first, next recruitment would be a captain for a start.
The other option is to dismantle it all and start from scratch and emulate the likes of Barca. No way am I getting rid of Mane, Salah, Coutinho, Gino- who all/some were part of that collapse, part of the Spurs debacle and part of the City picnic. No way! If we remove everyone else- then that's just about all we have. It's a MASSIVE overhaul to perform. That's prolly 500million in overhauliing and that won't buy you a top-tier squad who can equal the exploits of Barca, PSG, Madrid, Bayern Munich. Those are the teams with leaders throughout the pitch. We're arguing for a team with the power of the sun in their eyes and fire in their bellies and that's just not practical or realistic.
That is.. not an option for us- at least not now, which is why I'm advocating to at least start with the glaring obvious.. then we move on from there.
There are different approaches to tam building- either you fill your squid with strong mentalities or you fill them with talented "water-carriers" and throw in 3/4 winning mentalities in there. Either way- both works and currently prolly 90% of top teams follow the latter(and that's been working for more than a hundred years), while the rest prolly follow the former(I'm looking at ye, Barca..).