The point of the post is just that if you can get rid of most of the big operational problems with using server-side SQLite in a distributed application --- most notably, failing over and snapshotting --- then SQLite can occupy a much more interesting role in your stack than it's conventionally been assigned. SQLite has some very attractive properties that have been largely ignored because people assume they won't be able to scale it out and manage it. Well, you can scale it out and manage it. Now you've got an extremely simple database layer that's easy to reason about, doesn't require you to run a database server (or even a cache server) next to all your app instances, and happens to be extraordinarily fast.
Maybe it doesn't make sense for your app? There are probably lots of apps that really want Postgres and not SQLite. But the architecture we're proposing is one people historically haven't even considered. Now, they should.
I'm not sure "litestream replicate <file>" really costs a whole innovation token. It's just SQLite. You should get an innovation rebate for using it. :)