The original Hellblazer always had a very strong sense of community as a way to ground John, each run had its distinctive supporting characters and the theme of places like London or Newcastle bearing phantom scars, as John himself does, is a major part of almost every run in the 300 issues, even if it's just a minor haunting story. Hellblazer is like a soap opera. It's like Eastenders with ghosts. John isn't an occult detective, he's an occult handyman at best. He's a dodgy neighbour.
This is actually what made me kind of excited about him joining the main DC Universe. He'd have a whole ready-made community to play around in, but somewhere around his team-up with He-Man, me and John Constantine kind of parted ways.
Gotham After Midnight was a solid venture into those kinds of themes, and Constantine: The Hellblazer looked to be a promising fresh start that turned out to be very little. Neither really scratched that itch.
It's a bit sad, because it was always fun to check up on that guy and see what he was up to, but there hasn't really been any opportunities to do that lately. Poor sod.