Is ASR for real, or is it only for those sub $1k or even sub $2K?

ASR is not a place to identify good sounding gear. They do some simple electronic tests and make completely erroneous conclusions on sound quality. Ignore them.

Consult reviewers that base their recommendations on listening to the gear. Have a look at Stereophile, The Absolute Sound, and HiFi+. Not popular mags like Stereo Review. The three periodicals I referred to review very expensive to relatively inexpensive components. They have annual reviews of hundreds of good components. 
 

If you want to learn about high end audio sound and systems. I recommend The Complete Guide to High End Audio by Robert Harley.

ASR forum members reputation is that measurements are all that matters sonically - I highly suspect rationalization to justify not spending for better equipment.

The truth is that audio reproduction is non-exact, so sonic presentations are different depending on gear, the entire audio chain, the room, etc.  It’s always best to demo yourself to find what subjectively resonates with you.   

ASR is a good source of info to help find good performing gear cost effectively.  Is there more to it than that?  You get to decide. 

"They do some simple electronic tests and make completely erroneous conclusions on sound quality. Ignore them."

Indeed. They are also dismissive and extremely rude to anyone who does not agree with them.

They’re spec afficionados.  No subjective input allowed.  Why use your ears when you can print out a data sheet that tells you everything you need to know.   I find some of the info useful, but also find it hard to take that philosophy serious on an absolute basis.  I stopped buying gear based on specs in 1983.