Can SoC Processors be used as more powerful microcontrollers?
Looks available to me: Digikey. Parametric search is your friend.

Note that they tend to come in less convenient packages and not have integrated RAM, so your PCB design is a lot harder.

Note also that a 300MHz RISC processor can actually do quite a lot; that's roughly equivalent to a desktop computer of the late 90s. The only thing in your list that might be tricky is music decoding, and you can usually farm that off to a dedicated MP3/AAC decoder chip if you want. Or get it sent over the network in decompressed form. Certainly the web is full of people driving small touch panel weather station projects from Arduinos. Or the ever-present Raspberry Pi.