They could have just beamed or shuttled down to some Federation outpost along the way, such as the one on Delta Vega, and used their communication equipment.
I would classify this as a weakness, at worst a minor one.
Well lets think about that. If they had contacted Starfleet and received orders the decision would have been taken out of their hands and it would have no longer been "the Enterprise against the universe". Worse, whatever Starfleet's decision, Kirk wouldn't have met Spock Prime and wouldn't have taken command of the Enterprise.
In other words it would have derailed the plot the writers went with so it seems to be a decent sized plot hole.
So my acknowledgement that it is a weakness just isn't good for you? I'm afraid you're going to have to come up with a better reason to elevate it to a plot hole than the idea that it would have derailed the plot.
Actually, upon further reflection I have figured out how to repair almost all of the difficulties in this issue and the issue of jettisoning Kirk. What if Spock expected Kirk to warn Starfleet when he was picked up on Delta Vega? That would justify both jettisoning Kirk and moving the ship on to rendezvous with the fleet without further delay. That places the blame squarely on Scotty's shoulders for dereliction of duty in switching off his space beeper to be notified that he needed to go pick up a pod 14 clicks away from his outpost. This is something that I've already asserted to be in character for Scotty, as far as I'm concerned. He was, you know, pissed for being sent there.