Most OSS projects simply don’t have that kind of weight or discipline to follow SQLite’s footsteps.
It did not have to, they could(and some would argue probably should) have gone the normal copyright with public use license route. But I suspect that because US government code by default is in the public domain(the US government has means other than copyright to protect it's IP) and this code was originally written for a cancelled US government project. That was their default mindset when they wanted to release it.
Note that I am using a sort of editorial they here, I think it was largely the effort of one person.
It is probably telling that with fossil, a supporting project to sqlite, they went the more normal route and released it under copyright with a BSD type license.
I like the idea of public domain(some things belong to us collectively), but it does raise an interesting question if a private individual can place something in the public domain. Are you allowed to give up your rights?
SQLite is in a whole different league when it comes to funding, corporate support, etc. There are commercial contracts directly tied to its ongoing support and development. As far as I understand SQLite is Hwaci’s bread and butter.