What are the advantages to a Class A amp & what are the trade offs?

George, Krell never made a mono amp with the designation KSA.
they were KMA 100s and there were also KMA 50s and 200s. They all used fan powered chimney heat sinks and they were all class A to rated power. I owned a pair of KMA 100s for 20 years and they were great amps.

In simple word Fantastic listening pleasure just like going to an Opera house or Jazz bakery club in LA.  During winter its an alternative heater 

The Jazz Bakery isn't an ideal sounding venue.  I've frequented it half a dozen times.  Bob Wilber played there a decade ago and his sax and clarinet sounded peaky and bright, actually aggressive sounding, so unlike his playing style.  Locally, many churches and concert halls have great acoustics.  The absolute worst with a 5 second reverb time is the Queen of Angels Cathedral.  I've sung there four times and I couldn't hear myself in the choir with all that reverb.  My wife said it sounded like mush.

Class A amps are the least efficient kind. They are bigger heavier and draw more power (per watt output) than the rest so total cost of ownership is high. To make up for that you tend to want speakers that are more efficient. Quality full range hifi speakers that are also more efficient also tend to be larger, heavier and often more expensive as well.

Class A amps from reputable vendors are usually very highly regarded in terms of inherent sound quality.