Aren’t most pro audio speakers very high sensitivity?
Yes, most pro audio speakers feature high efficiency. Oh, I don't like the the term sensitivity for a loudspeaker, simply by the fact that a speaker is a converter; it converts an AC current into a sound wave. IMHO, it is more appropriate to use the word efficiency. I don't know who suddenly decided that efficiency was not right term but sensitivity was.
By the way, for the 12v trigger for a pro amp, Amazon have a
Xantech AC1 Controlled AC Outlet.
It has been discontinued by the manufacturer, but you can get one if you don't hesitate too long. They have a few left for around $115 apiece.
For your question about quiet pro amps, the QSC DCA (Digital Cinema Amp) Series are rather quiet amps. If you prefer Class A/B amps, the Model DCA1222 provides a clean 325 watts/ch at 4 ohms. It is cooled by a rather silent variable speed fan.
I am at present using two of those 2 channel amps for my front left and right actively biamped speaker enclosures. My listening position is 6 feet away from the fans and I can't hear them. I intend to purchase a third one to drive the front center system also in a biamplified configuration.
Those cinema amps are actually being used in many theaters in the US and in Canada and they provide an excellent and reliable performance. They are also manufactured in the USA. They are not normally sold in musician's or pro audio shops, but a few on line stores in California sell them or a distributor which you can find on QSC's website. For instance, the DCA1222 retails for over $900 in US but two stores in California were asking $729 when I recently looked on their websites.