I'm not sure how well that works as an explanation, though. Surely he would have used the techniques he had been taught and had seen his superiors using when he was a junior officer in training. I suppose there could be "shouting" and "non-shouting" schools of thought, but more likely there would be Starfleet-wide standards and best practices. Spock's shouting stands out because we never see it again from anybody.
There is one person giving orders on the bridge, normally the OOD. One person responsible for executing the order acknowledges it by repeating it back and adding "aye." Extra repetition is discouraged. If the captain wants to take over the conn from the OOD, he announces "I have the conn," the OOD acknowledges and then shuts up completely. The captain, XO and navigator can take the conn from the OOD at any time. That's why "captain on the bridge" is announced, it's a reminder to everyone to pay attention because the orders could start coming from a different person.
Repetition of orders by extra people would be more for relaying them in on-deck evolutions where people are spread out and wind, noise etc. get in the way (which is mostly done with hand radios nowadays).
My turn? "SEN-SOR BEAM ON!"
