Phew thanks for posting this, I thought it was just me who was thinking this!
You've definitely noticed something and I'd like to try to add my observations which might shed some light on this (or maybe not).
I've been aware of this for the last 10/20 years and tend to avoid people that go down this conversational path. As you have mentioned the problem is that there is a real scarcity of these people around.
We've recently moved out of London after having a kid along with what seems like half of London. We've moved to an area that is popular with these leavers.
Dare I say it but I have mentioned to my partner (who is from the place that we have now moved to) that if I had known I was moving to East Dulwich/Clapham then I wish we would have picked somewhere else. I'm joking of course (kind of).
From the people I've met who are from here (who are more my type of people), a lot less of them have these particular traits. Yummy Mummy, tiger parent (whatever the phrase is that is commonly used) seems to be less of a thing among people who are from here. Not that it isn't there, but the locals here really do seem to not have the same levels of self aggrandisement/boastfulness/mememe chat that I'm used to.
I also think it's an age thing which I noticed with my uni mates. Mid 30s is when you'll probably start to do well, get promoted, get more responsibility etc. Obvious caveat with those having a child/multiple children obvs! And it's at this point when I noticed egos starting to spin a bit out of control. As I'm a bit older, add on the fact that social media indulges the sad human trait that some people really want to be stars in their won lives and want to feel special, I think these issues bleed into each other.
But ultimately it comes down to one thing, is the person who you speak to have any sense of self deprecation as a tool of their chat? That appears to be the main marker that sets people apart for me at least. One of the people I have met down here who I really like is a classic yummy mummy type. University, lived in London and moved here, has a good job in property, has multiple kids, is successful and....takes the piss out of herself.
It's a very rare trait and one that is only to rare IMO. Oh well.