In TOS, this was not a big problem, as typically the ship was not
all that interested in what the landing party was doing. After all, the commander of the team was also the commander of the ship and the overall mission, and was on the spot already.
TOS also gave us every reason to believe that visual records were
being made - we saw some, e.g. in the teaser of "Friday's Child". Apparently, and in all simplicity, the tricorder was also a camcorder. Whether the capacity existed to send the imagery to the ship in real time... Well, why not? "Miri" suggested that uplinking was technologically somewhat challenging, but only to the degree of involving the hand communicators as a mediating agent.
TNG should really have thought this through when introducing the all-new
dramatic element of communication between away teams and the mission commander.