It'll sort of depend on how committed you are to solely wood fired central heating. If you have a system that will accept heat input from a gas boiler as well as from the solid fuel back boiler, then you can top up the central heating that way, otherwise I think your plumber is probably right. Your house must be pretty big to have 20 radiators... You're not going to get them more than tepid without a beast of a stove! Ok, so you're not going to have all of them switched on at once, right? But you'll still be heating the water in pipes between them. The sheer size of the system will be a serious challenge to a moderate boiler. Bear in mind , too, if you aim to use wood rather than coal in a multifuel stove, the output will be considerably less than the manufacturer's rating.
However... If you consider a very high heat output stove, you need to be clear about how much of that is space heating, and how much diverted to the back boiler. We have a small stove, carefully sized to the room, but when it's going full throttle, we do tend to wilt in the heat! If the rating is too high for your room, your sitting room will be made completely unusable in order to get the central heating working. And that's without even starting on the aesthetics...
I think you need to stop and ask yourself what your aims for this system really are. If its the aesthetics of a solid fuel stove, then get the size of stove you want to look at, either separate from the CH, or with a back boiler to contribute to a more complex system (with gas system boiler, maybe solar hot water too... Will require a pretty fancy hot water tank). If its all about renewables as fuel, consider a pellet boiler, which can be sited away from the living areas (though pellets are less convincing as carbon neutral fuel).