You have a more complex network setup actually. You have north-south traffic between your client->LB->servers. and you have east-west traffic between your servers for sqlite replication. Both happening on the same nodes and no isolation whatsoever. More things can go wrong and will require more tooling to disambiguate between different potential failures.
W.r.t security, you have same challenges to secure east/west vs north/south traffic. W.r.t # of connections, Postgres has a limit on number of connections for a reason – if you are running a multi-process or milt-thread app framework that's talking to sqlite, you have just traded connection limit to concurrent process/thread access limit to sqlite. I don't know if one is better than other – it all depends on your tooling to debug things when things inevitably fail at redline stress conditions.
You're technically right, which is to say: Not at all.
You don't replicate east-west with Litestream, you replicate north -> south where the "North" is your writer and your "South" is some S3-like service. Basically every application has "Some S3 Like Service" as a dependency now, so that's not a new network connection.
You make a really good point about trading Sqlite write limits to the limited number of Postgres connections. My comment is mostly about having to run a proxy, which is another service that ends up being a liability. Regardless, if you need multi-writers, then the obvious solution is Postgres.
"Both happening on the same nodes and no isolation whatsoever. More things can go wrong and will require more tooling to disambiguate between different potential failures."
As a Postgres fan, the extra Postgres service to me is a far bigger liability than Sqlite. The east-west networking is true for Postgres replication as well, so it's a wash to me.
W.r.t security, you have same challenges to secure east/west vs north/south traffic. W.r.t # of connections, Postgres has a limit on number of connections for a reason – if you are running a multi-process or milt-thread app framework that's talking to sqlite, you have just traded connection limit to concurrent process/thread access limit to sqlite. I don't know if one is better than other – it all depends on your tooling to debug things when things inevitably fail at redline stress conditions.