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

Class A may well have been superceded by other topologies. Even some chip gaincones sound very good. 
Sugden have made and continue to make, Class A amps. They're handmade in the UK. 
My introduction, as a musician, to class A was an epiphany. 
I built and listened to commercial class B amps at university.
I performed in a concert in a church with a large organ in 1974.
The concert was recorded. 
On playback the revelation was how every upper rank of the organ was crystal clear. There was no blurring I'd been accustomed to with other amplifiers.
My main instruments of study were piano and flute but I played a lot on pipe organ.
That was my epiphany. 
I've listened to a DIY Sugden 10w class A driving Lowther speakers. 
My degrees and diplomas are in classical music. 
I spent 30 yrs producing recordings of concerts for broadcast on national radio. 
We used proper commercial equipment with standard Neumann, b&k and akg microphones. 
My class A + Lowther combo was used as a reference. If the recording sounded good on them, then it was fine on anything. 
Our studios used B&W and Tannoy monitors, but most recordings were made in our mobile van. 

It depends on the Class A and whether it is tube based or transistor based but couple things are universally true.  

They are horribly inefficient and run very hot.  Due to that heat, they tend to require large heat sinks.  They tend to be very heavy and power consumption is very high.  Because they are so inefficient, they tend not to be that high power.  

Sound profile is a varied as there are amp companies.  I have heard Class A amps that are dark and warm and others that are bright and shrill.  Tube amps vary as much as transistor amps and careful pairing with your speakers is still required along with plenty of ventilation.  

@verdantaudio I’m glad Gryphon integrated two chimneys in the Colosseum, haha. The amp actually runs pretty cool on low bias, 30w Class A, because of the huge heatsinks, but it runs very hot at 165w Class A. Yes, I can hear a difference between the two.


 @mijostyn I will try that coffee. How much is it a pound? For those who wonder about my math to get to fifty five cents a cup it was $25/454g*10. I only use ten grams a day, that’s my dose.

@larrykell41, we used to have a nice Pasquini espresso machine and grinder in the office which was used on a $1 suggested contribution model. It worked well, providing artisan roasted beans, organic whole milk, and the occasional necessary parts. We were using double shots of 18-20 g per drink. The $1 didn’t account for energy use.
The espresso bar definitely made the office a better place and improved the barista skills, and coffee appreciation of many.

Perhaps a good stereo in an office space, for break time, would revitalize the love of good music reproduction?

A big advantage of Class A amps is that by the standards of any AB amp they have a hugely overbuilt power supply and they can drive low impedance loads without faltering.

One of my systems has a pair of Class A monoblocs that put out 45 watts a channel in stereo configuration, but 500 watts bridged into a 1 ohm load.  Hard for AB amps to match that.  They are also large and heavy, if that matters to you - mine are over 100 lbs. each.

If you don't run difficult loads, then the choice comes down to sound vs. power usage and heat production.  I really like the sound and still own 4 Class A amps, but I use an AB tube amp to run my main system which has quite efficient speakers.(92dB)