The "cleaner control" and "new mission" is where the innovation happens.
No. New mission usually means more maps unless you define the mission very broadly to include, e.g. all the objects involved in the mission or the rules that are followed. Cleaner control also merely means removing flaws that were inherent in the control or rule system. Unless you broaden any of those two definitions there's not going to be a whole lot of innovation there. What would leave those definitions? If new weapons and abilities (a popular addition to sequels) count as "new mission", wouldn't the waterpack do so, too?
The problem is that a sequel is supposed to expand upon what made the original game great, yes, but what makes the game great differs. You cannot deliver a blanket statement on what needs to be done to make a proper sequel. Besides, usually a game exploits practically everything that can be done within the boundaries of its ruleset and just adding more levels would lead to repetition, that's why the rleset must be expanded. However, there's no blanket way of saying what can be altered in a ruleset and what must remain the same. A sequel to Wario Ware would need to keep only a single rule: It must be comprised of a set of microgames. But you couldn't make a sequel to Mario Kart by only keeping the rule that it is a racer. Another problem is that the perception of which rules must be changed differ from person to person. Some want entire portions of the ruleset to be thrown out/altered, others freak out if even a physics glitch is removed. If, for example, a person doesn't like the combat system in an RPG they'll demand a different one in the sequel, but the people who liked it will oppose the change. Who should the developer listen to?