I have not used a medical messaging system, but if it's anything like the messages my bank or my insurance company sends on their own systems then these will look much more like text messages and less like emails. No place to "sign". No need to risk it looking like fraud. As for awkward conversations, I'd be shocked if many people don't experience circumstances where their doctors act as if they don't remember previous in-person conversations. They're seeing 25 patients a day for 3 minutes at a time after all.

The standard will evolve to something like clinic staff sending the messages which will be overseen/supervised by a medical doctor (who won't be involved in composing the messages or spend any time looking at them before or after they are sent). We'll see trials where the doctor who was supposed to be keeping an eye on the messages wasn't, and some flunky kills a patient by suggesting that drinking used engine oil will cure the sniffles. Keep in mind that the messages can be sent from anywhere too, technically no need to keep that onshore. May eventually get legislation that would guarantee that, but only after a wild west period that lasts a few years.