David, welcome! In answer to your question as to why more Thiel users don't use pure Class A amplification: cost. And heat.
To my ears, though typically advantageous, Class A is not the only criterion of the many upon which an amplifier's sound is determined.
Jim Thiel's power recommendations were based upon standard solid state 8 Ohm ratings (with a level of quality expected), where it could be assumed that the power doubled down as impedance halved, not the impedance load of the specific speaker.
Let's take your 3.7's
https://www.stereophile.com/content/thiel-cs37-loudspeaker-specifications
for example: with power recommendations given as 100 - 600 Watts per channel. Of course actual power needs will vary with rooms and desired volume levels amongst other things. But, for the sake of this post, let's fall on the old audiophile axiom that one should first consider starting with double the minimum power recommendation, which in the case of the 3.7's would be 200 Watts per channel. 200 Watts per channel of pure Class A amplification comes with some expense.
Many high quality amps runs their bias towards Class A before sliding into Class AB. For example I run my 3.5's with their recommend power of 50 Watts minimum 250 Watts maximum (with hints of 300 Watts max). My Threshold amplifier is rated at 250 Watts (8 Ohm) per channel. The first 20% (50 Watts) biased towards Class A, then sliding into Class AB. Now into my 3.5's 4 Ohm minimum impedance; as the impedance is halved, the power doubles to 500 Watts per channel, but the Class A bias output is halved to 25 Watts per channel.
This not only true for some Class AB amps. Some amps that claim pure Class A output really only do so in their standard 8 Ohm rating, but as the impedance halves and the power levels double; their Class A outputs halve as well, with the increased power correspondingly sliding into Class AB.
https://www.stereophile.com/content/threshold-stasis-sa12e-power-amplifier-page-2
Of course some amps that tout pure Class A output, really don't.
https://www.stereophile.com/content/krell-ksa-250-power-amplifier-when-class-class
We know that power consumption is not linear but rather exponential, and musical content can demand many, many times it's nominal power requirements. I haven't measured the bias output, but I suspect that much of the time my amp is behaving towards Class A bias. But now with the capability to cruise at 500 Watts per channel all day long (with short term headroom doubling that to 1000 Watts per channel).
Now some might suggest that some of these power recommendations into actual impedances are outrageously high. To those may I remind them that with Thiel's and most typical speakers for that matter, that as impedances drop and power output increases that speaker sensitivity decreases correspondingly. So for general comparisons one might see the wisdom of the standard 8 Ohm ratings. Or not?
Would I prefer more Class A output? Probably, double that would be dandy. All 500 Watts per channel into 4 Ohms Class A? Sure! But, for my money I'd probably move up the line in speakers first, and settle on less Class A output with Thiel CS 5i's.
Thiel's weren't made as cost no object super premium products, though in their time the CS 5's were knocking on the door. Given the cost of pure Class A with enough power to drive most Thiel's, some of which approach 2 Ohms (and some with challenging phase angles), I think many might find the money might be better off spent elsewhere. For example with the 3.7's, and given enough room, I can easily see someone spending the money on Thiel's own subwoofers before committing the funds towards up to 600 Watts of pure Class A amplification (if you could find it). As a general guide (and with adequate funds available), perhaps a reasonable starting point might be amplification meeting the minimum power recommendation with Class A and the maximum into power recommendation sliding into Class AB. If one could afford to provide the maximum power recommendation all in pure Class A output into actual minimum impedance load, perhaps all the better. But be prepared to pay!
