Genuine question - why is it a given that there will be latency issues? It looks like the satellites are only ~350 miles, or a little less than 2 light-milliseconds, from Earth's surface.
User -> Satellite -> multiple hops between satellites (as they are orbiting earth and the right one has to be selected to relay data to -> earth DNS servers -> multiple hops across internet -> satellite -> user
Additional latency is introduced due to satellites and the grid between the satellites, as well as complications from rotation of satellites.
All of that in general is comparable to the costs incurred on the ground from any other kind of network.
> complications from rotation of satellites
As far as a single routed packet is concerned, the satellites are stationary.