Regarding the Rotodyne concept, it wasn't so much that it was tip-driven that was the big point; it was that it was intended to convert in flight from a vertical take-off pure helicopter into an autogyro supplemented by fixed-wing lift. The idea was, the rotor would be powered for takeoff and initial acceleration, and then gradually a jet or propellors would first supplement and then take over completely from the thrust derived from the rotor; the rotor would segue from being powered (by the tip jets, but in concept there is no reason this wouldn't work essentially the same way if it were conventionally powered at the hub) and providing the thrust, to being powered just enough to counter its own drag, and then using the drag to maintain its rotation and thus lift while the tip jets (or central drive shaft!) shut down completely; meanwhile lift is gradually offloaded from the rotor to the fixed wings, the craft now being propelled entirely by props or jets like a conventional airplane (or autogyro). It's basically a glorified hopping autogyro.
I think a big part of the cleverness of using the tip jet was that using that rotor drive system rather than a conventional central-shaft-driven hub was that this system was only needed transitionally, for take-off and landing, and so trading off efficiency against lightness of the system unusually favored the tip-jet system; also, the compressed airflow was provided by the same engine that would in cruising flight provide the horizontal thrust, presumably as a jet engine. So the additional weight of the rotor drive system was the tip jets and the ducting to send the compressed air to feed them, and of course the fuel lines to the tip jets. As jet engines the tip jets were light and simple because their air intake came pre-supercharged by the central engine. I doubt they were very fuel-efficient! But they wouldn't have to be for temporary operation; the main thing is for them to be light, simple, and reliable.
Avoiding the reaction torque of a central drive shaft system is a nice bonus, but in principle if the Rotodyne did use such a conventional system instead, then again I'd think a single central engine (or set of two or three of them as is customary on heavier helicopters, in case one turbine fails) could initially be geared to drive the rotor conventionally, then gradually another clutch engages and more and more torque is being taken up by propellors driven through shafts instead, and the load on the central rotor shaft lightens and eventually the freewheel clutch disengages the rotor from it and that shaft is then declutched from the engine, stopped, and the craft flies as a prop-driven autogyro--again the same engine that initially lifted it as a helicopter turboshaft is now serving as a turboprop. With such a system you'd have to have a tail rotor until the central rotor driveshaft is disengaged, and now you'd have it being dead weight and drag. But I've seen pictures of helicopters that used a pusher ducted fan with vanes to divert the thrust to the side to provide the countertorque; presumably that was such an approach to the conversion from helicopter to autogyro in flight.
In all of these cases, the idea is to get the capability of vertical lift without the penalty of high power associated with much lower airspeeds than an airplane with much less power can achieve. Compared to a pure airplane even the Rotodyne would suffer, with more weight, lower speeds, heavier engines, and poorer fuel economy, but by unloading the rotor I believe they were able to mitigate the consequence of the massive asymmetry of lift between the advancing and retreating rotor that severely limits the forward airspeed of a pure helicopter; it was still a problem and a limit but a less severe one with most lift now coming from the wing, so they could attain higher airspeeds and thus use more of the installed power necessary for vertical lift. I suspect that using the autogyro mode of airflow to drive the rotor might automatically tend to slow the rotor RPM as forward airspeeds increase, thus preventing the forward advancing blade from exceeding the speed of sound--but that's just a musing guess of mine.
Another advantage of the Fairly approach of tip-jets was that in rotor takeoff, the whole engine was the central gas generator plus the tip jets; considered as a whole, this consumed more fuel and generated more power than the central engine alone; whereas in cruising flight only the central engine set would be in use and so as a prop-driver or direct jet engine, it was less powerful--thus a better, lighter, more economical match for the power requirements of cruise flight. I admit the alternative of a single engine driving both rotor and props through gearboxes and shafts doesn't offer that clever economy.
I agree it would have been cool for the technology to be developed!