I don't understand why SQLite has become popular for stuff like a website where it is not really a good fit due to concurrency.

If HA, replication, etc isn't needed, installing and running PostgreSQL or MySQL isn't much more complicated than SQLite.

> where it is not really a good fit due to concurrency

I'm the first to admit that concurrency is and always has been a point of contention in SQLite. But, on the other hand, when your concurrency problem is "we have to co-ordinate many small-ish inserts from web site users" I'm being told that due to the in-process nature of SQLite and overall good performance of inserts you can do A LOT even with SQLite's concurrency model. IOW manages to be fast enough for concurrency not to be the problem.