Yes, but, running a "yep, I can hear that" test is a lot less interesting and motivating, for most people, than being able to actually do something quasi-practical with the radio link.
I think it'd open up the possibilities of like, weather balloons streaming their telemetry openly, while ensuring the data they're reporting hasn't been forged, or letting anyone send random commands to it.
That's already allowed, and commonly done.
97.113(a)(4) doesn't say "no cryptography", it says (in part):
>> No amateur station shall transmit [...] messages encoded for the purpose of obscuring their meaning.
The scheme you're describing doesn't obscure the meaning of your transmissions, so it is perfectly legal.
https://www.ecfr.gov/current/title-47/chapter-I/subchapter-D...
You miss the point, it is not about communication as in having a conversation. HAM radio is about testing technical skills of setting it up and being able to test those technical skills to set up communication channel.
If you want to have encryption go to enterprise solutions and restricted bandwidths. Encryption will make asshole companies to use bandwidth for their use without paying and will make all spectrum suck.
That is why you have call signs and all communications open for everyone to listen to because it is for public experimentation not for some private chats or data exchange.