There are three levels of anonymity: anonymity to the general public, to Apple, and to a state-level actor. Anonymity to the general public is very easy, incorporate a company behind some of the shell corporation mumbo jumbo that any corporate lawyer can prep for you, it will cost $ but it will be easy. Anonymity from Apple could probably be pulled off by incorporating in a country with fairly weak transparency and h…
I'd say "totally impractical/impossible for regular individuals".
As James Mickens so eloquently put it:
If your adversary is the Mossad, YOU’RE GONNA DIE AND THERE’S NOTHING THAT YOU CAN DO ABOUT IT. The Mossad is not intimidated by the fact that you employ https://. If the Mossad wants your data, they’re going to use a drone to replace your cellphone with a piece of uranium that’s shaped like a cellphone, and when you die of tumors filled with tumors, they’re going to hold a press conference and say “It wasn’t us” as they wear t-shirts that say “IT WAS DEFINITELY US,” and then they’re going to buy all of your stuff at your estate sale so that they can directly look at the photos of your vacation instead of reading your insipid emails about them. -- https://www.usenix.org/system/files/1401_08-12_mickens.pdf
Some of us enjoy cosplaying extreme privacy nuts, or engaging in recreational paranoia. But don't for a minute kid yourself into believing you stand a chance against the NSA (or your jurisdiction's equivalent).