One of my previous employers was using SQLite as a large distributed database - they had their own custom sharding strategy, but essentially the idea was to shard A accounts * B tables * C num_of_days with a .db file for every shard.
When I first came and saw it, it...did not sound right. But I didn't want to be the guy who comes in and says "you are doing it wrong" month 1. So I went along with it.
Of course, eventually problems started to pop up. I distinctly remember that the ingestion (happening via a lot of Kafka consumers) throughput was high enough that SQLite started to crumble and even saw WAL overruns, data loss etc. Fortunately, it wasn't "real" production yet.
I suggested we move to Postgres and was eventually able to convince everyone from engineers to leadership. We moved to a custom sharded Postgres (9.6 at the time). This was in 2016. I spoke to people at the place last month, and it's still humming along nicely.
This isn't to illustrate anything bad about SQLite, to be clear! I like it for what it does. Just to show at least 1 use case where it was a bad fit.
SQLite was a tempting first answer, but what solved it was Postgres, and we eventually offloaded a lot of aggregation tables to Clickhouse and turned the whole thing into a warehouse where the events got logged.