Supabase at is minimum providing a PostgreSQL server, pooler (they started on pgbouncer, how their own) and a PostREST API, and support, backup, logging etc. You can be doing serious business and not have the time/people to run these reliably self-hosted. They also provide Auth almost to the Auth0 level and Edge functions like Vercel, S3 like storage (sharing the db's permission system), and websocket/presence backed by Elixir. TBH they are a compelling value, at least for us.

What is serious business? I think supabase can scale brilliantly, and it doesn't lock you in, if you have need for some special infra you can build and integrate it, I don't know but you could possibly even use FDW to access a postgres you run yourself.

Also they can't run on AWS postgres with all their postgres plug-ins AFAIK.

The point of "cheaper to host everything yourself" is a lot higher than what most estimate.

My only concern is that is supabase goes out of business or go evil you're gonna have a bad time, however everything is open-source

My former place ran a lot of RDS Postgres but also loved Supabase. It's more than just hosted DB because it has loads of value adds like web-based table editing, auth, edge functions, row-level security, easy hooks and triggers. We were capable of operating RDS but the cost of operations in dev hours was high. Supabase was super easy for moderate price and readily compatible with our RDS and Redshift.