Encryption is also not allowed by law, since it's public spectrum. Allowing encryption would be akin to allowing somebody to just build a structure in the middle of a public park. That takes away usable recreational area from other people.
Further, allowing anonymity & strong encryption on amateur radio is possible.
If you're claiming there's a difference somehow in the use of spectrum bandwidth, I'm not seeing it; meaning even with anonymity and strong encryption it would be possible to manage bandwidth abuse.
In any case, it's the same argument for not allowing automobiles on walking paths: sure, it'd probably work, but it sort of takes the fun and utility out of it for other people. Encrypted messages converted to sound for transmission over the air sounds horrible, and for somebody that's scanning through the band, landing on that monstrosity is very unpleasant. Also,if you are transmitting encrypted traffic, you are by definition doing so at the exclusion of every other ham; they can't know what you're transmitting, and they can't transmit there. Plus, ham bands are 100% noncommercial, so there's also no way to enforce that rule.
The purpose of the ham bands is not for you to pass your tinfoil wrapped messages to other similarly paranoid people. If you want that, use unlicensed spectrum. You can pass whatever kind of traffic you want there, assuming you're not causing interference.