It is implied that at least in theory, the promise is to use them with the similar total complexity (like numberr of parameters and amount of required calculati

It is implied that at least in theory, the promise is to use them with the similar total complexity (like numberr of parameters and amount of required calculation), in which case yes we do want the most general data structure possible. If we can have a more general data structure that provides similar performance characteristics, it is easier to apply, to debug, to understand, and it likely means that we have found something more fundamental about the underlying world in general.