I'm talking about relatively simple cases like spinning up a phpbb3 (web forum) instance. The minute you have multiple users writing comments at the same time from different apache/php instances is the minute your SQLite database starts to fall over.
Every write (aka: every comment post) is an exclusive write on SQLite. A full lock that prevents other processes from reading. (Ex: User#1 writes a comment, but User#2 hits refresh. These two items will be sequential if you use SQLite... when normally they'd be concurrent in most other databases)
------
SQLite is an exceptionally good database for many purposes. But it has its weaknesses. There's a reason why MySQL and PostgreSQL exist after all.