The barbican is odd, mainly because its the only brutalist "council housing estate" that actually mostly worked as intended[1]
If you compare the layout/style to say the haygate estate (https://www.bbc.co.uk/news/uk-england-london-13092349 where attack the block was filmed) or the lesser known aylesbury estate, its more enclosed, but no less brutalist.
What is different is that unlike the southwark estates, it always had the original tenancy requirements upheld (either by tenant action, location or happenstance.) [2]
This meant that it didn't have the massive abandonment in the 90s, left to rot throughout the 00s. The quality of the haygate estate was actually pretty high, secure entry, gardens for the low rise, district heating, trees and playgrounds.
What was fucked up was that the heygate was a dumping ground for undesirables. this mean a spiral of drugs, crime and antisocial behaviour. The barbican escaped most of this because people were too fucking posh.
The social life of the barbican was upheld because of the huge amounts of money poured into the cultural centres that are hidden (and I mean hidden, the place is a fucking impossible maze) Most of the tenant social clubs were disbanded on the other estates, and the halls sold off or leased out to businesses.
In many way, the barbican isn't a great estate in terms of building quality. Its the same as any >60s council property. They all had to be big enough, have a separate kitchen and decent storage.
[1] well its not a mixed class housing estate, its all full of posh design types, and a handful of tenants left over from the 80s
[2] to get a council house, you had to be of good standing, and have a job. It wasn't a place to dumo drugadicts or problem families.
TLDR: the barbican is decent housing because it was reasonably well maintained, and wasn't filled with families in distress, or habitual criminals. We need to build more council estates to the same standard, with the same rules as the 60s.