> LTE was a huge battery drain at first because they weren't integrated
No, the modem/SoC integration is not a big factor. Having an internal communication inside a single SoC will always be a bit better than going through an external interface, but it's not a significant impact when compared to the total phone power consumption. As other have said, iPhones have an external modem and are fine. Qualcomm insisted on this because they had it, and they're good at marketing.
LTE was a drain at first for the same reason 3G was a drain at first. Cellular standards are designed to have a long life, and are over dimensioned initially. Then Moore law and other optimizations kicks in and make things more acceptable. This is intentional, otherwise the standard would not make the best use of technology over time. And this is something where we need to keep an eye for 5G: Moore law, strictly speaking (higher density for the least cost process. One can still get better, for a higher price) is over. Hopefully 5G will have properly taken this into account.
But then for 5G a big part of the power will be in the RF front-end, with all those antennas. Here too it'll be interesting to see how it evolves over time.