I know some people who are loud all the time. They don't mean to be; they just are, even when talking naturally. They're very extroverted, so they love chatting, and my God, they dominate a room all the bloody time. I can't hear myself think in their presence, so I either join in with their conversation or leave - it's impossible to ignore them. Yes, they get even louder after they've drunk something.
I suspect this kind of projection is something to do with lung capacity or something else physical, so potentially something that runs in their families. Having never met their blood relatives, I can't prove the theory, but if a whole group of them got together for a meal, I'd bet money they'd drown people out. And I don't think it's malicious at all or something they can tone down without whispering - I probably wouldn't expect them to realise they were overpowering a restaurant, as they wouldn't even be shouting.
I'm in two minds about the music.
If the music were turned down, yes, no one would need to shout. But it could have been providing background noise to muffle the words of your noisy table, and it might actually make your table more annoying to everyone else.
Nine is a large table. But it's generally not large enough for private dining. Putting a big group in a side room is often the solution as it keeps their noise contained and it makes it easier to manage the orders. But I think you usually need a dozen people to make it viable. Plus, the restaurant you were at might not have had any such areas built into its design.
Actually, where were you sat? If you were at a table in the middle of the restaurant, they planned that pretty poorly, as the noise was always likely to bother people. You don't want to hide groups in the worst bit next to the toilets, but you do want to think about acoustics when seating people, and I imagine you had made a reservation in advance, given the party number.
It's easier to move a table of two than tell a table of nine to behave better, so for the waiter to speak to you, I think more people must have been upset than you thought and that you were louder than you thought.
I wouldn't complain, but as you say, I probably wouldn't go back. Not necessarily because the restaurant has done anything wrong, but because it's not compatible with want you want to do. (And because it sounds quite expensive - and for something to be that pricey, I don't just want the food to be good, I want everything to be good!)