We already have it with YugabyteDB, which is open source (unlike Neon), but doesn't seem to be the success story it should have been. At least I've heard barely a peep about it. Maybe they're not so great at marketing.
Yugabyte is architected similarly to other similar databases, with an SQL layer on top of a distributed, replicated key/value store based on RocksDB. The different being that the SQL layer is Postgres.
Yugabyte tightly couples the two, though, though it seems like this is mostly for convenience, in that the "TServer" (tablet server) is managed by Yugabyte itself. I wonder if it could support an architecture more similar to TiDB, where the storage is independently scalable from compute.
CockroachDB and TiDB are based on a similar design, but Yugabyte stands out as being a "real" Postgres. It even supports normal Postgres extensions via "CREATE EXTENSION".