Indeed, somebody at Starfleet should have worried ("one of our 12 starships is missing!"). But I found most of the script for this particular episode disturbing.
"Quickly! Communications Officer!: Since I'm stuck down here for the rest of my life and since everyone onboard is about to perish, in your last few minutes, patch my communicator through to the main shipboard communications controls so that I can call up to the ship whenever I want and fire up the ship's subspace radio remotely from here and transmit messages to Starfleet on a regular basis if I so desire!"
"Wait a minute, Captain Tracey! You mean make it so you can use your communicator from down there on the planet to access the much higher powered ship's communications system to check in with Starfleet Command on a regular basis in order to trick them into believing that everything is hunky-dory with you? I don't think that kind of technology is even possible in the 24th century! That's just madness!"
"Oh, I think it
is possible, Lieutenant. I remember how way back in the 21st century people were able to use their hand-held telephones to call their TiVos and other devices in their 'smart houses' to get them to do all kinds of stuff. It must be possible here in the 24th century to set up a similar thing with a couple of button pushes--but we're running out of time!"
"I'm not so sure it can be done, sir. You mean make it so that you, down on the planet, can use the
Exeter as a relay station to contact others besides just us--if you wanted to deceive them into thinking all is well?"
"Yes, that's
exactly what I mean. I think it
is possible: I remember hearing about how Captain Kirk was down on Planet Q once and was able to contact his communications officer Lieutenant Uhura on board the
Enterprise to ask her to put him through to Captain Jon Daily of the AstraI Queen on orbit station. I don't think the
Enterprise's capabilities are all that more sophisticated than ours on the
Exeter, and it sounds like all Lieutenat Uhura had to do was something that we ourselves could rig up to be done in an automated fashion by running what would pbobably be a very small shell script."