Isn't that exactly what Starlink and other similar services are doing? They're putting swarms of communication satellites into LEO for this very purpose.

Starlinks are placed in LEO at 550km, which would have a theoretical 3.6ms round-trip ping at the speed of light. That is not a "very long latency".

No, it's not, it's doing the "swarm" thing I mentioned to get around the limitations of GEO. The downside is now you have a big swarm of satellites in orbit, interfering with telescopes, and regularly falling into the atmosphere. Also, there's a significant cost to maintaining this system, and its total bandwidth capability is limited.