Which bit is expensive? if it is steel discs and you can't produce them yourself then perhaps you are right. If you include resin then that also adds to the cost.

If you are thinking in terms of what I consider the expensive bits, magnets and copper, then you will not produce a cheaper machine by using open magnetic circuits.

As for the cooling, depends on how you mount it and what protection you give the coils.

For a given cost of copper and magnet your open flux design will have a lower efficiency and to maintain the same heat then you will get less out than an equivalent dual rotor. You can always build anything efficient enough not to over heat with any design if you want to but you will need to include serious inefficiency somewhere in the line to avoid stall if you want to directly connect it to a battery. The only way to include the loss in the alternator is to adopt cooling methods that can dissipate that crazy loss. Your idea may be a bit better than a dual rotor but if you do other things to make it robust you will be little better off.

As I say everyone has their choices as to the best method, much depends on local conditions and availability of materials and facilities. This method will produce a good machine with good low wind performance but in the hands of most people will not be the cheapest or most convenient. You alone must decide.