But they do care what GPS reference time is. Which are satellites very much dependent on holding an accurate position in the sky (which is dependent on the Earth's rotational speed, which changes, which is why we have leap seconds).

So go figure: which part of this system should be broken because people keep ignoring that leap seconds happen?

Actually, GPS time is not adjusted for leap seconds:

http://tycho.usno.navy.mil/leapsec.html

That's neither here nor there: GPS receivers, and the GPS satellites, do broadcast the leap-second insertions (though they don't reset their own clocks, they simply maintain the differential as additional information).