This is a great idea, but unfortunately, it wouldn't work in all situations. For instance, if I down someone and want to continue the RP, like kidnapping them, they could still use the radio and potentially reveal everything happening, even though they're down, (A big probability that they will stall RP of taking the radio until they give detailed callouts)
From my perspective, this would eliminate post-injury RP entirely, as players would simply finish off anyone they've downed to prevent them from making callouts to their teammates.
One suggestion I have is that players could still be able to make phone calls, as they can actually receive them while injured.