This great question discusses the disadvantages of a lighter flywheel:
It seems to me that the disadvantages could all be resolved in modern engine control systems by modulating the fuel and FBW throttle positions. Why isn't this done? The lighter fly wheel would lead to increased engine performance and fuel economy.
Well for one thing the mass of the flywheel is what it is because manufacturers have to strike a balance between performance and drive-ability and emissions figures. A lighter flywheel would require the car to idle at higher RPM's to keep from stalling because the inertia of the flywheel is what keeps the engine firing when you're not on the gas.
So yes, it can fairly easily be done, but the reason it's not is because most consumers will not be happy with a car that idles at 1000RPM and the relevant country's ministry of transport/EPA/whatever won't like all the polarbears you're killing.
As for dual-mass flywheels. They're great and all, but they're hellishly expensive to replace WHEN (not if) they go bad. E.g. my Subaru is pretty old school with its single mass flywheel, but it would cost a third to replace it compared to the dual-mass setup in the equivalent Mazda.
The hardest part of a lightweight flywheel is getting used to taking off. Its like learning to drive a stick again. You need to rev it a bit more, or you will stall. There may be some 'Anti stall technology' you can use, especially with drive by wire. The shorter shift window pairs nicely with a short throw shifter. Again, takes a bit of getting used to.
The ECU should be able to compensate some of the 'jerkiness.' When going on/off the gas, there is less momentum, so the RPM changes more rapidly and causes a jerk. The ECU could open the throttle a little when coming off the gas, or open it slower when getting on the gas.
I think the real approach to this is not adjusting the throttle, it's by changing the valve timing to synthetically lower the compression ratio. This will decrease the opposition to the crankshaft turning, conserving its momentum just like the flywheel does. Leaving the intake valve open during the first part of the compression stroke should do it.
