MHL is an option but it only fixes the number of pins issue. It has the same problem as HDMI out: you need a transceiver capable of multi-Gbit data rates. You also have to get the video output to the transceiver. Its not the easiest thing to do inside a phone, its really not the easiest thing to do when your next phone release is focused on 'thinner and lighter'.

Apple already made a strong commitment to AirPlay, so they already had a focus on building a fast, smooth, low power encoder that could encode the entire screen. Once encoded, the stream is probably only a few Mbit/s, a data rate that can easily be transmitted with single ended protocols like SPI. Almost all SoCs already have multiple SPI buses so no need to change any hardware.

Their solution may seem inelegant to some, but I think it is great. They managed to support a feature with almost zero hardware costs on the core device (depending on how you assign the lightning connector). A feature that I'm willing to bet only a very small % of all users will ever use. That is a big win, not having to dump extra hardware into a device that only 5% of all users will ever activate does great things for your margin and design flexibility.