I think it probably feels embarrassing to have the volume of your voice pointed out. No matter how gently, it probably feels like a rebuke. I think it is better, though, to tell the Loud Person that you are bothered, rather than avoid them, try to tolerate it and become increasingly annoyed, or talk to others about it behind Loud's back. Saying something might cause momentary embarrassment, but improve the relationship long term.
However, if the response is, "Sorry, that is just the way I am," then you know that the behavior won't change and can make any necessary modifications. I do think that response doesn't take the feelings of others into consideration.