Other characters often read aloud to Hanks' the messages they receive over these other modes. Was there a technological limitation preventing multiple telephones from being used? Was it a matter of construction cost?
Further, did the signal lights and radio morse code have specific use cases? And did each of these modes of communication have advantages over eachother (besides the obvious disadvantage of the signal lights not working out of visual range)?
The film takes place in the Battle of the Atlantic, mostly within the Mid-Atlantic Gap.
Good guesses. I'll adapt an answer I've posted elsewhere on the subject.
While it takes a few creative liberties, with one notable exception Greyhound is actually pretty accurate in how it represents convoy communications.
The telephone represents Talk Between Ships (TBS) radio. This was the precursor to modern day marine VHF radio in the same overall frequency range (156-174 MHz), although it often transmitted at vastly higher power (up to 1000 watts) than the 25 watt sets available today. Since VHF requires line of sight to be routinely received - it can bounce off the atmosphere and travel long distances, just not consistently - unless you're on top of the CN tower and have well over a 50 mile horizon that kind of power generally causes more problems than it solves.
TBS, though, was generally pretty limited in its uses, especially since it was almost completely insecure - voice scramblers didn't come along for another 20 years, meaning that the best that could be done was very weak encryption like letter transposition. In short, most of the conversations between the warship commanders probably wouldn't have taken place over TBS, especially once they were aware that without a doubt the channels were being monitored by the enemy. However, it's a creative decision I agree with; even if it might have been more accurate, solely using semaphore and signal lights to communicate takes away the urgency, and I really liked how almost all we know about fellow escorts Dick, Harry and Eagle comes from a few shots and the disembodied voices on VHF.
But there's even a bigger creative liberty: circa the February 1942 setting of the movie, TBS was only just starting to be installed on ships like the Mahan class USS Keeling portrayed in the book that the movie is adapted from. TBS sets were expensive and both the US and British Navy prioritized them for their capital ships and their task forces rather than escorts, so that all the warships involved would even have TBS is a bit of a stretch at that point in the war.
That said, to address your question directly, the reason that the convoy received its orders via semaphore or signal light is that given the rarity and expense of the VHF sets at the time, none of the escorted ships - or even the rescue ship - would have had them installed until perhaps very late in the war. The movie's portrayal is pretty accurate as to how an escort would have communicated: instructing the commodore of the merchant vessels via semaphore or signal lights (depending on time of day and position) and then having him propagate the commands to the rest of the fleet.
The one exception? The wolfpack's taunting is not just jarring and somewhat out of place but extremely unlikely to have taken place. Some U Boats might have had equipment installed to receive transmissions in the VHF range, but their transmitters were pretty much restricted to HF. It's a strange decision in an otherwise well constructed movie.