Well, you're using an extremely limited global resource. Blasting your voice around the world with 1,500 watts behind it is something that not everybody can do at once. So we need some sort of internationally agreeable rule set. The compromises include no encryption, required licensing, individual identification, no political speech, and others. But what we get in return is pretty cool: I can talk to somebody in Japan in a truly peer-to-peer fashion, using nothing but our own hardware in our own homes and the natural electromagnetic properties of the atmosphere.
If encryption were allowed on the ham bands, they would probably become dominated by general purpose digital communications; likely to the exclusion of their current purpose.
Your conversations aren't just not encrypted, they're totally public. That's unacceptable for most communications.
Take everything you do on a phone call, over SMS, and over the Internet. Subtract anything personal, anything business related, anything involving copyright (e.g. watching a movie or listening to a song, even if you own it), and anything you don't want associated with your identity (anonymous blogging). Also, I forgot to mention that broadcasting is also disallowed. You couldn't just start telling poetry on a frequency without regard to anybody who may or may not be listening. You also can't use the bands for any commercial purpose.
Anyway, after subtracting all that, what your left with is what people use the band for today. Which, I suppose, could still be considered "general purpose." But when I said "general purpose digital communications," what I had in mind were the sorts of things you use email or the web for. By volume, mostly music, videos, porn, ads, and private business operations.
Eh, this is not exactly true. Digital traffic, even encrypted, is easily recognizable unless the protocol is explicitly designed to look like noise (which is very uncommon/unheard of). It's true that encrypted data is (ideally) distributed like noise, but digital noise doesn't necessarily look or sound at all like ambient RF noise and there is also usually some non-encrypted packet structure wrapping the encrypted payload by necessity. You can very easily identify on e.g. DMR or P25 by ear if you know what to listen for, encrypted or not.
The restrictions have nothing to do with preventing people from transmitting noise. Transmitting encrypted on amateur radio stations was originally not allowed because of espionage concerns in the earlier days of amateur radio, and has stuck around largely to prevent abuse. Allowing unencrypted but encoded transmissions makes sense in that context, as long as the protocol is published.
If encryption were allowed on the ham bands, they would probably become dominated by general purpose digital communications; likely to the exclusion of their current purpose.