“Control” and “responsive” are not absolute terms in the real world. If by control one means temperature stability, for example, then thick aluminum or even steel beats typical copper cookware thickness hands down. You CAN use thick copper, of course, but you better be rich. Think Mauviel Cuprinox prices ... (YOW!) If by responsive one mean *fast* response to temperature changes, then a reasonably thin section of copper is terrific, but then, so are most thinner materials. Yes, copper is more thermally conductive, but as the metals get thinner this is a matter of dimishing returns. Conductivity and heat capacity (also considering mass) interplay in complex ways. Introduce layering and alloys and things get a LOT more complicated.
There is no “best” cookware type for all purposes just as there isn’t one type of control or responsiveness. Looking at commercial cooking ... which isn’t necessarily what you want to emulate at home ... shows some strong patterns, such as carbon steel pans for high-temp, fast and responsive cooking - but a commercial kitchen also uses high-BTU ranges, doesn’t have to consider heat retention as a result, and is prepared to clean up the resulting spatter and baked-on mess - for which they have flunkies (I’ve been one, and it isn’t fun). What is best at home depends on how and what you cook as well as what you cook it on.
Example: I use seasoned cast iron for searing. I do have to heat the skillet carefully and for longer than I would with another type of pan, but the heat retention once hot is terrific and makes up for my typically low household gas range output. Maintenance is dead simple, as searing actually helps maintain the seasoning. Could I use stainless? ABSOLUTELY! In fact, an All-Clad skillet would work nearly as well. But since I prefer to maintain my stainless cookware unseasoned, maintenance for this use is more of a chore. (You can season stainless just like you can cast iron or carbon steel, though no-one does for some reason.) Thick copper would be terrific, too, but I don’t want to maintain it ... inside AND out, no less. And any kind of thin pan, of whatever metal, wouldn’t stand up to the abuse for long. Every kind of cooking, every approach to technique, every circumstance, and even every dish (to stretch the point) carries its own considerations.