I love Days. Would I want every KH game to be like it? No (and to me it's biggest flaw was that it went on too long, even if I personally really liked getting a lot of insights on the characters that way, and think the other games suffer from a lack of that), but for what it was I think it was a breath of fresh air that I needed.
Also, I went into the game hating Roxas, Axel, and being prepared to despise Xion, and I left it with Roxas and Xion in my top three KH characters and liking Axel (the Days trio is also the most believable and most balanced to me, aside from SDG), so that's definitely good writing and characterization to me.
I think Days for sure definitely has the best character development and characterization in the series, and I think that a lot of people (even if they hate the rest of the game) will mostly agree with that (aside from Riku and his arc, I mean; and Naminé I guess, too).
The story is kind of stupid, I'll admit, but for the characters I can deal with it. I even like Days more than KHII, because KHII had a great story idea that was executed horribly, and Days had a story... that wasn't that great, but with characters and writing that at least made me care about them.
The biggest offender is definitely the gameplay. It's just too clunky. For a while I used to like it over CoM's style, but that's not true for me anymore:/
But, yeah: I really like Days. And I know a lot of casuals who do. My friend Michael, for instance, hates Sora and mostly plays the games for Riku, but he enjoyed getting to play as Roxas in Days, and getting to see Axel (who he likes), and he grew to like Xion.
The multiplayer was also a really fun idea, and I had a lot of fun doing that with my friends who had the games, personally.
I also really like Xion, and think she's definitely one of the better female characters in this series writing-wise (with even more depth than Aqua thus far), and I'm just glad about her being included in the series in general, because this franchise needs more girls.
And on a side note (so not trying to turn this into a Xion debate, btw), I will say that I think a lot of hate towards her is unjustified. Like, the problems that I see most people have with her are things that like 99.9% of the cast has (numerous of these characters being introduced after she was, like Vanitas), so to me it's not right to blame her for these things if you're also not going to blame the entire cast for them.
And even if you don't like her... I don't get why people would want her to disappear completely. Ask for writing about her to be better in the next installments, fine--or for a better use and role for her--but to get rid of one of the only six (really four) girls in a sea of twenty-six men is insane to me (I'm sorry).
I've also never seen a fandom, other than the KH one, that would dislike a character for not being absolutely central to the plot. I don't see people complaining about Asha/Tiara from the Game of Thrones series, and she doesn't add that much, either. But do I still like her, her story, and what she brings to the world (and characters like Theon)? You bet! And I feel the same way about Xion in KH.
Plus, not everything needs to be about plot. I like Xion for what she brings to the characters, like Roxas. And I honestly think that's more important atm, because KH is almost just plot plot plot, with no focus on the characters and their interactions at all, but I digress.
I do have to admit that I very rarely reply Days, though, and I sort of dread doing so because of the gameplay. More often than not these days, I'll settle for the movie (even if I have some issues with the movie, think it changed some of the feel of Days and made it into another beast entirely--becoming the "Axel show"--instead of about Roxas and Xion like the game was), but I can also say that about CoM, Coded, and DDD, so that's not really a sign to me that Days is bad to me. To me, at least.
Because tbh, I play these games for the story, and sometimes if I could get the story without even playing the game, I'd be very tempted (at least if we're talking about some of the harder things--like secret bosses--to get the secret movie and that kind of thing, that a lot of times I can't be bothered to do).
Edit: Also, though I don't think the Disney segments were that good, I did appreciate that they were at least new stories and not recycles of the movie plot for the millionth time. I even enjoyed some of them. Seeing Aladdin trying to solve his own problems, without relying on the Genie, was particularly nice.
And no one can deny that the localization staff totally killed it with adding humor to this game.
I'd even say that I think this game might be truer to Nomura's vision than any of the other KH titles in some ways (since he actually wrote a lot of the dialogue himself), and that it really shines through, explains things better than some of the other games, and makes it all the more enjoyable for me that way. Though I can understand why others wouldn't agree with that.