Agreed. However, a diesel (or any recip) uses that energy differently than a turbine. A turbine may have a better thermal efficiency than a reciprocating engine. But the smaller turbines use up to 50% of that energy to keep the engine running. Which is not very efficient. Recip engines loose less power to keep the engine alive. If given the same amount of fuel the recip engine will make more power.
As far as cost. I can see diesels getting expensive but I hardly think it will surpass the cost of a turbine. Of a gas engine, maybe. But a gas engine that would make enough power to lift the planned Eurocopter would not be feasible and or economic.