Many of the upcoming very light jets or personal jets have speeds of 300-400 knots. Would it not be more economical to fly at the same speeds with piston or turboprop engines instead?
All things being equal the turboprop would certainly be the more economical. Prop-less aircraft generally enjoy greater passenger appeal than propeller aircraft though. Aircraft like the Bombardier Dash 8 series 400 and the Piaggio Avanti are good examples of short-haul, fast as jets point-to-point, economical turbo-prop aircraft. They enjoy much quieter cabins than the earlier generation of prop aircraft – the Dash 8-400 has an active noise supression system and the Avanti has the advantage of rear-located engines driving aft-facing propellers – the noise is effectively ‘left behind’.