Well, it's not so much innovation as it is change...which might seem like a question of semantics, as the two terms are often user interchangably - you even did as much in your opening post - but I think it's important to clarify in these instances the difference between the two...or, at least it is for me if I'm going to type out a tl;dr response.
Innovation, to me at least, has always been something that begins from nothing; it's an entirely new and unique idea. Like when a new IP surfaces, or you get an entirely new genre, if you want to take it one step further. In series - hell, in the game industry at large if you want to be cynical about it, which I won't for the time being because I want to stick to my point for a change - innovation is non-existent for the most part. You have a base, and aspects of it are altered or refined as the years go by. It's change...and evolution I suppose, but I really don't like using that word when evolution is supposed to be something positive and a lot of the time evolution in gaming is garbage, so. Change, because it's a non-loaded term with no positive or negative connotations other than what the individual attaches to it. Innovation is about new ideas, change is about refining existing ideas. Unless the core gameplay is different, there is no innovation, only change.
So, with all that premable said: I think that changes, whether they're positively or negatively received, are always a good thing for video games, because it is only through these small changes a better experience as a whole can come about; only be refining the idea can you improve it and, whilst you might seriously balls it up along the way (hi, Final Fantasy XIII, Skyward Sword, Tales of Zestiria...numerous others) you hopefully won't make the same mistake twice...or you'll improve upon the idea you had and make it workable (FFXIII-2, for all its faults, WAS an improvement over FFXIII in the gameplay department) and provide a better experience. Only by trying can you know if something is a good idea or not. Any good developer worth anything at all takes their fan feedback of changes into account, and either retains them in the next instalment in the franchise with additions and enhancements, or removes them entirely.
What makes a "better game" in any franchise is down to personal opinion, though. Ask someone what their favourite title is in any long-standing fandom and why and you're just asking for a flame war to kick off, because different people like different things. All you can really do is go by the majority and, if you're considerate, present the option to turn these features on or off in accordance with your personal preference and playstyle. The best small changes are applied, then refined as the series develops so that they're not quite as intrusive as they were previously, or are better incorporated into the game.
I didn't like the game, but I will applaud Awakening's choice to provide multiple difficulty modes, so people could customise it to whatever degree they chose...they were all still pathetically easy options no matter what you picked if you'd ever played an SRPG before, but it was a nice gesture, and one that should be replicated in titles like Pokemon, which took Easy Mode and Challenge Mode out after B2W2 and have yet to reincorporate them, which is a damn shame in my opinion. That said, I think in a way they HAVE considered that, just in a different fashion: play the sixth generation titles with the EXP share off, then play them with it on. You'll spend longer grinding in the former playthrough if you want to have as easy a time winning as you did in the former, and artificial difficulty is all Pokemon and Fire Emblem have ever had: when every challenge in a game can be overcome by grinding, that isn't true difficulty.
Continuing on with Pokemon - because that's the only slightly positive comment I have to make of Fire Emblem; I strongly dislike the series - I think that the changes they've made to the core gameplay have been mostly successful: things are a lot smoother, a lot more convenient, and not quite as maddening as they used to be. When the gameplay is fundamentally the same across multiple games, the little things add up, and Pokemon is a lot more convenient and streamlined now than it used to be. These thing have been so small and introduced with no fanfare at all, yet I think they're the changes that matter most, because...well, can you imagine how painful playing the game would be without them?
Back in the day, you couldn't move Pokemon in your PC, your inventory was a mess, you couldn't even see how much EXP you needed for the next level without checking in the menu. The games have had some serious balance issues more recently - the random encounter and EXP growth rate in Black and White were diabolical, and in X/Y and ORAS they're cranked up to eleven in the opposite direction to make levelling ridiculously fast - but all those little, core gameplay changes that have come about over the years, have done nothing but improve the experience, at least in my opinion. The bigger, more noticeable stuff like seasons, day and night, the physical/special split and so on, are a little more questionable and depend really on where you entered the franchise and what you want out of the games, but the changes that have been made for convenience...well, they're small, but the wrath would be considerable if they had been removed.
I feel like I should have some grand conclusion for this incoherent babble, so I guess I'd just say I think the best way to go about change is to introduce it, promote it, see what the feedback is, then work on improving it...and NEVER force it. Let us turn it off if we choose; not everyone wants to have it thrown in their faces and forced upon them; some people don't like change at all, and that's OK...even if they could be a bit more gracious about it. But the little things that improve core gameplay and make it more accessible for newer and older players alike, the stuff nobody draws attention to...keep working on it. Games in a series should be judged based on their individual merit, but a series of games should be considered a work-in-progress, and NOT a perfected formula that gets rehashed every year or so with different weapon/character skins, different maps, and some shiny new graphics and background music.
