These are weird reasons. You can just install Postgres or MySQL locally too. Connection pool tuning certainly isn't anything you have to worry about for a moderate write volume. You don't ever need to upgrade the database if you don't want to, since you're not publicly exposing it. There's obviously no replication lag if you're not replicating, which you wouldn't be with a single server.
The reason you don't usually choose SQLite for the web is future-proofing. If you're totally sure you'll always stay single-server forever, then sure, go for it. But if there's even a tiny chance you'll ever need to expand to multiple web servers, then you'll wish you'd chosen a client-server database from the start. And again, you can run Postgres/MySQL locally, on even the tiniest cheapest VPS, basically just as easily as using SQLite.