I think I disagree with this. Your functors should generally be pure, and for pure functors applicative is a nicer semantics.
Consider the case of a set implemented as a binary tree. The type of such a set should be parametrised by the type of the elements and the ordering used. With applicative functors this is the case as your set type will be `Set(O).t` where `O` is a structure containing the type and the ordering. With generative functors each individual set type is abstract -- so the type itself is not parameterised by the ordering.
You could consider this to be just an example of what you are calling "Modular Type Classes", but there doesn't need to be a system of implicit module parameters for it to be useful.
Consider the case of a set implemented as a binary tree. The type of such a set should be parametrised by the type of the elements and the ordering used. With applicative functors this is the case as your set type will be `Set(O).t` where `O` is a structure containing the type and the ordering. With generative functors each individual set type is abstract -- so the type itself is not parameterised by the ordering.
You could consider this to be just an example of what you are calling "Modular Type Classes", but there doesn't need to be a system of implicit module parameters for it to be useful.