The only diseases they can spread are from plant root to plant root by chewing on roots, and they generally don't feed that way and don't have any living plants to bite in the compost pile. As for the compost, they are no worse than earthworms in that they feed on decaying organic matter. Personally I don't want worms in my compost because they digest the decomposed organic matter that I am trying so hard to make for the plants. My plants can grow in 50 pounds of organic matter, they can't do much with the 1 lb of worm flesh that grew by eating that 50 lbs.

The fungus gnats are a natural part of the system. If they weren't there something is probably wrong with the compost or else it is finished decomposing.

Fungus Gnats can exist only in a fairly wet environment so the presence of Fungus Gnats in a compost pile is an indication it is too wet. Turn the pile and add dryer material, but no more moisture, and they will die.