I don't think there's any need to look at games from the developer's perspective because their goal is different from the consumer's.
I used to think that what makes a good sequel was pretty clear but now it's a bit strange.
Take the Hitman series, because that's imo a great example of how sequels should be done.
Each game has:
A) better or somewhat improved graphics. That's the perfect way to go about it. The art direction remains, the feel and atmosphere of the game remains but the game looks prettier.
B) attempted to streamline the interface (not as in "make easy to use for retards by removing functionality and options") but as in easier to do the same shit you could do in the previous games. That's perfect.
C) used the same formula and improved on it. The thing is that the formula has to be good, but when I'm buying a sequel I'm buying it because I liked the previous game. This is the consumer's point of view, fuck what the developers think about "making it available to a larger audience", I don't care and you don't care either, it's not our problem. Do you go "Oh man I wish they'd stop making Fifa about football and introduced shooting, then I'd certainly start buying it" ???
D) they made lots of quality of life changes and played around with the mechanics in order to improve the game, e.g. the ability to upgrade your weapons in BM, improved the melee combat, etc.
So the answer is that it should be very faithful because the consumer either doesn't care in the first place or wants more and better of the same.
Now there's a problem with longer running franchises. Again, Hitman solved it perfectly: when you're tired of making your great games, run the franchise to the ground by shitting all over it with the last game.
Or you know, make bigger changes that don't fuck up the core gameplay.
Heroes of Might and Magic:
all the first 3 games were exactly the same with gradual improvements in all their aspects until you got to 3. There's very little to improve on in that game to warrant making a sequel, because those previous games take hundreds of hours to play and enjoy and if you're a fan of the game, that's practically all you'll ever need. Now you want something a bit newer, fresh. So yeah, it makes sense to change things and I think Heroes 4 is great, it is controversial but I don't understand what the fans would actually want. Heroes 3 with more UI options and prettier graphics? That's not enough as you've put a thousand hours into the exactly same game over years.
In every game there's plenty to improve and that's what the sequels are for. Improve the graphics, improve the interface, add functionality and options to the gameplay and be very respectful of the (presumably successful) theme of the first game. That's how you get your fans to like the next game. If you've run out of things to improve except for the graphics, then start changing shit around, take a new angle at the similar thing but not when every person who likes your game just wants more of the same, that means there was still room for improvement.