Failing to connect those dots is (unfortunately) what keeps many, many people from moving their otherwise private conversations to a more private channel. I think you're right that it bears mentioning.
Signal and Threema seem to be known for good UX and viability as everyday messengers.
There was this table: https://www.messenger-matrix.de/messenger-matrix-en.html
Get as many of your contacts onto Signal as you can. Disable the displaying of message text within device notifications from within the Signal app settings (for both Android and iOS).