The governments have not and would not in the future allow the goal of improving international goodwill if the data being passed were encrypted because that's essentially legalized spy radios. In the past governments have made ham radio illegal from time to time just because of one time pads for example. If the whole point of the service is to have a service that uses self policing such that it doesn't require extensive monitoring by spy agencies and as such should not be banned for budgetary reasons...
Some non-USA governments have or had draconian postal and radio regulation such that it would be very tempting to bypass them via encrypted radio, such that they have an entire postal budget's worth of justification to enforce the general ham radio theme of "brief messages of a personal, non-commercial nature"
The issue of "brief messages of a personal, non-commercial nature" is significant; take for example the message:
"Have a nice day, geofft"
1) I mean it (like, why not?)
2) There's no logical argument how or why that message transfer would be improved by encryption. There's no possible way that info transfer could be improved by being sent as FGSHR HKSVN OSJVS SDFWE SAFDS AFDJS using an Enigma machine or similar tech. I mean, it would be kinda cool one time, but a pointless drag in the long run.
3) There are plenty of existing FCC regulated services to handle safely sending your credit card number over radio, so you have the burden of explaining why you won't use those existing services if you insist on giving me your credit card number instead of something more appropriate like "you too have a nice day". Like... if you want to transfer credit card numbers instead of having a polite conversation, why are you here anyway?
A better analogy than SSH or HTTPS would be banning IRC vertical spam of encrypted text. If you want to pay your bills online, technically you could spam the heck out of a popular IRC channel by flooding with some kind of BASE64 encoded TLS stream connected to your bank and your web browser via two gateways, but if you try that you're going to get kicked from the IRC network and told to use HTTPS which ironically already exists and works perfectly and was designed for that specific task. Or even worse analogy, picture me flooding a HN article with posts containing TCPIP packets from me logging into my local electric company trying to pay my electric bill, while the rest of you are trying to have a perfectly normal English language conversation about radio regulation surrounded by my vertical spam.
In summary the main difference is radio bandwidth is finite and we often operate at the limits, while internet bandwidth (from a human perspective) is essentially infinite. Also public utility land lines obey map and country boundaries, but radio waves can not.