The state can never fit on just a single machine, unless you're perfectly confident that single machine will never fail :)
Distributed consistency as discussed in this blog post is not really about scaling write throughput (which is the problem solved by horizontal/vertical partitioning), but rather about keeping replicas in sync with each other, seeing the same state. The usual suspects, MySQL and Postgres, don't really have any sort of replication that's totally synchronous (although they're getting there[1, 2]).
As for scaling writes, I agree that chopping up your Postgres database is the safest choice for now, but it's generally true that this is hacky, and kind of a pain to architect your application around it. Solutions like Spanner and FaunaDB aim to free the application developer from this burden, without having to give up the large feature set of relational databases by using a NoSQL database.
[1] https://dev.mysql.com/doc/refman/5.7/en/group-replication.ht...
[2] http://paquier.xyz/postgresql-2/postgres-10-quorum-sync/