Remakes aren't about redefining the genre, they're about redefining a single game. Whilst the changes might be minimal, systems do get refined and improved upon as the years go by. If you've played any remake (or even some HD remasters) that have had even the smallest amount of effort put into them you can see that the experience is, whilst not completely different, not as painful or awkward as it would be if you got out your old console and played the original. It's about enhancing a title to bring it up to the current standards, to make it a more enjoyable experience, to correct the flaws found in the original title in the gameplay; whatever.
A lot of games don't age well at all, or their gameplay systems get improved upon a lot in a relatively short space of time, making them look extremely dated as a result. Remaking those titles to remove those flaws isn't a bad thing, and it can be extremely beneficial as well, as it allows those who didn't play the titles the first go around to experence them in a more complete, up-to-date fashion. Those who want to play it again can do so without digging up their old consoles, as well. It depends entirely on the age of the title and what gets changed, in my opinion. Something like Ratchet and Clank, released on the PS2 in 2002 - fourteen years ago - more than warrants an updated remake. I've not played either title yet, but I'm willing to bet that the gameplay of the PS4 version is significantly better than the PS2 version. Whether or not the story is altered in any way is irrelevant - if it's a remake, you don't expect huge changes to the story.
This generation is a good example of things done wrong though. The number of "HD collections" we've had of games that haven't really needed them - The Last Of Us, Dishonored God of War III, Tomb Raider, and soon the Batman Arkham and BioShock games - that have in no meaningful way enhanced the experience is pretty awful. These are the kinds of things that should be frowned upon, rather than remakes/HD remasters of games several years old that are now pretty dated and have room for improvement.
The industry has always taken baby steps when it comes to improving gameplay, and that is only partially due to the attitude towards nostalgia. Yes, it's a problem that people only really want more of the same until they get bored of it, and new ideas are generally frowned upon. But it's only really a AAA and Nintendo problem. You can totally ignore it if you so choose and there is plenty out there that will cater to you.