Tips to help:
Firstly - Schmoozing/networking is usually a way of life for those that do it well, not something you turn on and off. It is usually in people’s DNA, they enjoy it, they make other people enjoy speaking to them/helping them. They cats the net wide - it occurs all day with everyone - with the person serving you coffee (‘mmm, you always make it perfectly’), the person in the lift (‘nice shoes’), their boss, their co-workers, their hairdresser. It’s part of their personality, and that’s why they are good at it. It isn’t inauthentic, they can genuinely and easily connect with people over small things.
In work settings or high stress social settings they can look like they are network the boss or the higher level people, and that is true, but really they are so confident and practiced at this, that when everyone else is on best behaviour (and nervous and quiet) in front of the big boss, they already have a confident, practiced charm ready and are themselves - resulting in them networking the boss because no one else is really talking to them like a human.
So this tip is really saying it’s a way of life. You can’t just turn it on and off again, as 1) you won’t be practiced enough, 2) the whole point is to cast the net wide. You don’t know that the woman in the coffee shop’s mother has an apartment that needs a caretaker in central London for 6 months, you need to be her friend before that comes up. Likewise, your friend’s old school friend isn’t going to put your name forward for a job at her company unless she has heard about you for awhile and likes you. So you will network and not get anywhere unless you do it all the time.
It’s a way of life. And if you aren’t comfortable (as it sounds like this isn't you), it will be a pretty miserable life, as you’ll always have to be turned to this setting. Whereas other people find it as easy as breathing and can’t turn it off.
Secondly - you have to cast the net wide for any return
Thirdly - you have to romance your life, and romance the returns you get. Things have to be painted as wonderful, regardless of truth. The central London flat might be full of mould, have drilling next to it and have screaming neighbours, but it has to be the best thing ever, else you don’t get offered anything else. The job has to be the best ever (even if it’s the mailroom), and/or if you leave it has to be for the even-better greatest thing ever (even if that is another mail room). If you don’t, people think you are ungrateful and you don’t get another offer, also you need people to envy and want you in their lives, hence the offers to help.
Finally, it is a precarious existence. You don’t have the luxury of turning down the flat or the job as you have no other options and no $ in the bank. You can’t chose where to live or what job exactly, you have to take what comes up. This is fine when you are young, but later in life you want some autonomy over your life. As you have said in your OP, one of these people has no home, job and no $ in the bank. So doing this hasn’t gotten him very far, has it? But because he romances his own life, you are now questioning whether his way is better!
Judging from your post, (and I say this kindly), I don’t think this is for you. I think your ‘heritage’ streak would mean this would all make you unhappy and you would come to dread interactions with people. But having said that, I would try and shift your rigid stance on networking/schmoozing and engage in it abit. Knowing more people and having strong social connections is always a good thing, even if it doesn’t lead to jobs or flats, it sometimes leads to new partners, new friends, more people……and I think Covid has taught us that more of that is a good thing.