LCD displays were (almost) always the type of screens used in phones until several years ago. Super AMOLED displays eventually came out on the market in high-end product lines (like the Samsung Galaxy S series).
The OLED technology, while expensive, was being offered at competitive prices and was already helping to usher in curved screens, lower power consumption (hence better battery life), thinner phones, crisper image quality, more even backlighting, and less motion blur.
iPhones haven’t gotten those yet, although the quality of iPhone screens has been on par with their OLED competitors, so there wasn’t actually anything wrong with them. However, it appears that Apple may switch to OLED (i’m not sure which variant of OLED) screens in iPhones in 2020, along with 5G. So it’s looking to be a big year for iPhones!
The timing makes sense, as manufacturers are coming out with foldable (and even rollable) displays. This may result in larger tablet-sized phones that can just fold to fit into your pocket. You can thank thin-film inkjet printing technology for that, as OLED screens are (at least sometimes) printed onto a substrate with inkjet printers).
People like large screens, but they also need to fit into their pockets. That will always be a challenge, and foldable displays are just the next step (not the last) in addressing that challenge. Maybe a wearable screen in the form of glasses or projection technology will come next. In such a case, phones would be able to get smaller without compromising your viewing experience.