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

At the end of the day, it is your ears that decide.  Class A has certain very distinct attributes that factor into its choice.

I have reasonably inefficient speakers (planars) that require a bit more power / current than is typically availabke from Class A amps.   

If I were running efficient speakers I would most certainly audition both Class A SS as well as tube amps and lwt my ears and wallet make the choice.

The beauty of this hobby is the myriad of choices we have on the journey.  Let no one criticize what your ears tell you as it is your money and your preferences based upon informed (read as having auditioned the choice) decision. 

Threshold 400A class A

I believe it's a push pull 100w Class-A/B amp. And with those heat sinks, about a max of 15w of Class-A,  with rail volts for 100w Class-B.

Cheers George 

Depending on your equiptment and you ears you will appreciate Class A more or less.  For me there is a relaxing and smoothness character to Class A.
I moved from a 540 watt Class D to 60 watt Class A to drive my Maggie 3.7i's.  I liked the Class D over the Class A/B Levinson. The 60 watt Class A has the current to drive the Maggies as loud as my wife will allow but not to the volume of the Class D.  I dont miss the Class D.  The Class A has much more umph and detail to the low end.  The Class A sounds better at all volumes.
I was worried about the heat but in my 20 x 25 room in Southern Ca. it has not been an issue.  I leave them on 24/7. The room is a little warm on warm days but it gets that way in the summer anyway.  I also have 2 tube preamps with a combined 10 tubes that are both on when I listen.  In a small room it may be an issue.
If you can afford Class A you wont likly go back to A/B or D.

@sfischer1 

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

I have one, but it is only my office.  Actually I have an office cat and a Hi-Fi in my office.  Also a Barista coffee machine close at hand.
The Hi-Fi is single source - a Technics SL1210 turntable.  Other components are Ayon Pre, ATC power and Spendor D1 standmounts.  To be honest there is not great synergy but the sound is passable.  It sure looks cool though, and clients love the LPs dotting the office.  In order to up to cool factor I need to have some tubes showing.  The Ayon Pre is a tube based pre-amp but the tubes are all internal.  I want glowing bottles!

MPG on home audio?   Best music?