Yes, as long as the key is available. For instance, we use WPA keys for our HAMnet microwave links, but using a well-known key that's publicly known.
D-Star and PACTOR are proprietary, undocumented algorithms but you're allowed to use them because devices implementing them are commercially available.
Our links are essentially standard 5 GHz wifi, but on licensed bands with higher tx power, and we don't want random people to connect to them. A WPA key mitigates that without breaking any regulations.
Mainly a mitigation against curious people with Ubiquiti equipment, which makes it way too easy to disable country restrictions and find and connect to our links in licensed bands :-)
You can easily find it on a public website if you know what you're looking for. It's only meant to deter people who click the "Scan" button on their equipment.
Well depending on what is broadcast, it might have a regular structure and perhaps there's some reason you'd want to randomize the broadcast signal. Maybe some highly specific noise in the environment that happens to resonate with the signal structure?
Alternatively there might be protocols which have mandatory encryption as part of their specification. Or you might be using a combined encryption-authentication mode, but only for the purpose of authentication on ham radio.
D-Star and PACTOR are proprietary, undocumented algorithms but you're allowed to use them because devices implementing them are commercially available.