[Gravityloss]

Yes. In the past turbines were very inefficient. Much higher compression ratio and thus efficiency nowadays. But piston engines have also improved. One problem with jets is that they don't scale down so well because of clearance issues.

Also they might need a secondary system to take energy from the hot exhaust gases. GE has proposed supercritical CO2 cycles for that. Could get total efficiency close to diesel, maintenance windows might be more frequent though.

This thread tells how you can run some jet engines on gasoline, though some pumps need to take that into account since it doesn't lubricate as well as kerosene. https://www.airliners.net/forum/viewtopic.php?t=751755