I've seen both the groundwork done for the FFX/X-2 Remaster and the ReMIXes and they are fundamentally different.
Almost the entire codebase was reworked in case the FF Remasters, something that had to be done to get good Vita ports. I can't prove it but I think that a PS4 port was projected from the beginning.
I'm definitely not gonna argue the port wasn't an idea from the beginning. X-3 was already an idea by then and if it comes out, it will undoubtedly be on PS4, making FFXHD a perfect candidate for said console.
The ReMIXes on the other hand are still pretty much the PS2 games they were (with the expection of BBS and the two movies obviously). In the case of the original Kingdom Hearts there wasn't even a way around it, because the source code and all original assets were lost.
Then and there SE should have made the decision to give KH, KHRECOM and KHII a propper remake, like they did with FFX and FFX-2, but they decided against it for reasons unbeknownst to us.
Honestly, I found the graphical styles and the things they did touch up on in KH1 and KH2 to be incredible. The games looked much better than their previous incarnations and I still feel could truly fit on the PS4.
Re:CoM, however, wasn't a bad port but a lazy-ish port that could have used more time to fix both the problems with the original as well as the problems the HD Remaster faced, such as not using any remastered music from 1.5, as well as looking graphically inferior when compared to KH1 and Days.
Birth by Sleep, while feeling great on a home console, still felt very much like a handheld game and honestly felt like little was done while porting it to make it mesh more well together with the other titles.
So, I do agree Re:CoM and Bbs could use some toucing up (
especially BbS). But I think KH1 and KH2 are fine as is. They look gorgeous.
However, FFXHD wasn't a remake. It was a Remaster. Did they touch up on quite a lot of stuff? Yeah. But it was still the same game, not a remake. Like how KH1 and KH2 were touched up as Remasters.
tl;dr This isn't about some glitches, this is really about how these games were ported in the first place.
Honestly, I thought part of what you meant was about glitches, which still is an issue they need to address for the PS4/Xbone port.