Since they already have this setting, one wonders why it is not trivial to extend it to allow remapping of all the available buttons.

The left and right button (plus scroll wheel these days) are standardized and pretty much guaranteed to work on arbitrary USB mice because otherwise users would revolt. Even reliable support for the middle button was a matter of luck for a long time, years ago (that was before scroll wheels were a thing).

Everything else the OS can't really expect to work. There's a reason why vendors of such advanced input devices provide their own config tools for Windows and macOS: both systems don't even try to support that clusterfuck out of the box.

After looking at the USB HID protocol for mice, I see what you mean. I was making the assumption that the button was detected by the OS and just not mappable by the user, but the protocol doesn't specify past the first 3 buttons so that isn't necessarily true.