Dark Souls is amazing and has virtually no flaws in my eyes, but boy I'd sure go back to it and revoke the entire Capra Demon boss fight from scratch. It's literally one of the most atrociously designed bosses from the whole franchise: extremely big boss that occupies a quarter of the map? Check. Small, cramped space with almost zero thought put into it? Check. Two stupidly annoying dogs that attack at random and probably caused a lot of people to break their controllers in half? Check.

Making the area bigger and removing the dogs altogether (or just situating the boss further away so that he can't just come for the cheap shot if dogs have you stunned, and giving you a chance to defend yourself) is what I'd do.

Star Fox Zero - 2 vehicles only: Arwing and Landmaster and no control gimmick. In fact keep the exact same controls and camera from N64.  It could also use a graphical revamp since it looks from 2 gens ago. 

FFXIII - This game is released with a different name, for a different/new franchise, and everything works just fine that way. 

Pokemon Sun/Moon:
- Skippable scenes - One thing I cant stand (and why I struggle replaying this game...) Is the forced scenes that explain things you already know. Too much time wasted for the game to even start. 
- Better Alolan Dex - The Alolan dex offers little variety and its very short.  
- Better stats for the new pokemon - To keep it short, most new pokemon are useless because of terrible stat distribution. 
- No hau - Replace Hau with literally any other stereotype and it works better. I dont like rivals that are your "friends". I like rivals that antagonize you. 
- Less overpowered pokemon - Meaning,  no focus on Ultra Beast/Legendary/Mythical/Whichever name you are comfortable with. 
- Super training is still part of game - Change the manner it works if you want, but this game seriously lacks content for competitive play and the lack of Super training hurts.  
- Better post game content. 

Dark Souls 2 - The lore of this game, I think should be more linked to the overall lore of the franchise, but most importantly... 32 bosses are too many, and most of which are meaningless, its a drag. A big plus of the DS franchise is supposed to be the memorable boss fights and its not the case with this game. Lets purge that number down to 20. We dont need bosses who are not linked to the lore and we dont need redundant or useless boss fights like 2 dragonriders, 2 royal rats boss fighs (Even if 1 is not really a rat, lol)  the sentry, even the gargoyles and def. the congregation boss fight can go away, to name the first ones that come to mind. 

Remove motion controls from Skyward Sword, and you fight the Imprisoned 1 or 2 or 10 times less than in the original

I'd change the title to "How would you do it?" I reads now as "How did you do it?"

Kid Icarus Uprising

- Make it a Star Fox game

Star Fox Zero

- Make it a new IP

Super Mario Odyssey

- Make it a Donkey Kong game

...I think you get my drift.

Metroid Prime Federation Force:

- I'd fire everyone that had a hand in this game and call it a day.

Tales of Symphonia: Dawn of the New World

take out the Symphonia name, world and characters.
maybe even take out the Tales of title.

easy way to make a terrible sequel into a decent game.

I was thinking of you and this reply when I ventured into this thread and read the OP.

Tales of Symphonia: Dawn of the New World:
Focus on the fact that the two sides of the world do not get along, and use Lloyd as the main character, trying to keep the world together, more serious tone. Also push the focus back on him not having any love interest (Namely not the one they gave him), but hinting it any option still possible. Exspheres are still being used for evil, and are enhanced. 

No Emil, No Fake Lloyd crap. 

Glad I didn't disappointed you

Fire Emblem Radiant Dawn, considered the hardest game in the franchise doesn't need a whole lot to make it better, cause Iran already amazing, but I would definitely add two chapters to the first part of the game and increase the levels of some of the characters you get in the first part, because the Liberation Army tends to be pretty useless unless you abuse EXP with them. And that's just annoying. Also online play and the ability to replay chapters would be nice.