Admins don’t ever close the tool, it’s always open on some RDP. Devs have different usage patterns.
SSMS is super duper nice if you’re an admin or a power SQL server user/dev. Nothing I’ve seen in Postgres world is comparable.
What you are describing is access via a PAM. Via RDP is one way to accessing it.
The only thing I wish they'd do with SSMS is add scaling support to the app... It's a bit small for my usage most of the time.
I've started using the extensions for VS Code a lot since they killed the separate code based SQL studio app. I also use a SQLite extension, though I wish the SQLite extension worked a bit more like the MS SQL extension does. Overall they're both nice.
Definitely different workflows for Devs vs DBAs though.. and you're right, DBAs don't really close SSMS, that said, I think the VS Code extension(s) are better for most dev usage.