I guess because that adds extra complexity that isn't inherently necessary and can be added on top, plus it eats resources. You'll spend the cycles either way basically, at least this way it's optional. I don't bother with a file indexer because with SSDs nowadays, find is pretty fast, and how often do you search for files anyway?

Linux has APIs to get notified on file system events (fanotify, inotify) which would allow such a service to update itself whenever files are created/delete immediately, but locate is way older than that, from the 80s. I think popular DEs have something like that.

There's also ways to search for specific files that come with packages (e.g. dpkg -S), because the package manager already maintains an index of files that were installed by it, so you can use that for most stuff outside /home.

They do. You look at it every time you see the contents of your disk. It's just organised in a tree to make path based lookups fast and locate organises its database differently to make fast basename lookups.