All of the past versions of "space internet" have been geostationary orbit, which is around 25,000-26,000 miles above sea level. The new iterations, such as SpaceX's idea, is to use many many more microsats and put them in LEO. Low Earth Orbit is closer to 750 or so miles above sea level. Since the ping latency of geostationary sat internet is around 500-700ms, it would be massively less for low earth orbit.

The two technical issues I'm aware of are the sheer number of satellites required for LEO internet, and the fact that you can't point your dish at a single place. There would need to be some sort of actuator or omnidirectional receiver for tracking to satellites at every client site. This makes the installation a bit trickier, but the ping times should be entirely reasonable provided someone gets the funding to put hundreds of satellites into an internet constellation.