There are only a couple of issues with OLED and it's getting worked out over the next few years. hopefully if apple get into OLED they should get sorted quicker.
1) sub pixel matrix, they're wonky and often pentile.
2) ghosting, it's getting better but image retention is still an issue.
3) blue shift, i'm sure apple can fix it but that the OLED pixels are't equal in life and brightness causes many other issues.
4) Brightness, OLED can't be as bright as an LED without drawing a lot more power, especially on white bright UI like iOS
5) Unrealistic colours. To show off OLED as better most makers hype the saturation and contrast and sharpening. But I like many don't want weird colours, we want accuracy over the lifetime of the device without artefacts.
6) Price/scale. New factories need to open for it to be viable for apple to consider.
The downsides are pretty big still but there are plenty of advantages that make it the next step, but boy do IPS displays keep getting better too.
most of those were remedied last version in the S6 generation. But true for older ones.
1) The benefit of going 1440p, especially with Pentile arrangements is to prevent the Pentile arrangement from causing blockiness. when you're PPI is so ridiculously high, well beyond the threshold that you see with the naked eye (and not just at it). you don't have to worry much about a Pentile layout.
2) Ghosting / Burnin is a non-issue. Most users will not run their displays in the way that stores displays are run (100% brightness 24/7 on static images). LCD suffers from the same thing under similar conditions (I've ruined a couple TVs accidentally over my lifespan on pause menues)
3) No blue shifting on the S6 display. But was terrible on the Note II. not all shifting is 100% though, S6 for example can have a very very very fine "pink" shift on white under some angles. This is an area that can always be improved.
4) You'd be surprised how bright the S6 and S7 now have been rated at. Though I can't speak for power draw.
5) This is a misnomer and is software driven, not display driven. Samsung is notorious for "vivid unrealistic colours", but what most people don't realize is that this is a setting in Touchwiz that can be turned off. By default Samsung phones ship with what is called "Dynamic" colour mode, which does oversaturate contrast and colour. But in the settings is a "standard" and "photo" mode. The Photo mode has been tested to be just as accurate as LCD displays in it's RGB colourspace. As Anandtech tested during their S6 tests, that it was one of the most accurate and best displays they had ever tested.
6) Amen to this. But like any new tech, Economies of scale should help. Apple going OLED will only help the entire market make it cheaper to produce (Since they'd be ordering on such a large scale)