No, the loudness is a whole separate dimension. 99% of the time, there's no need to be loud in public. Not when you're talking on the phone (the microphones on a phone work great!), not when you're having a conversation with one or two other people close to you. Not when talking to Siri (etc). You can talk quietly in a place that isn't very loud, and in a place like an airport you can talk just loud enough to be clearly heard -- there's no need to shout or to project your voice.

There are exceptions to this -- of course nobody expects you to worry about your volume at a concert between sets, at a sporting event, etc. But people who speak very loudly everywhere are annoying to everyone around them.