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.

It's perfectly legal to transmit noise-like signals such as digital voice, DVB-S2 and OFDM. You just can't encrypt the content.