Why not the piano as a reference for bass

Played clarinet from 5th through 12th and keyboards in a garage band in the late 60s early 70s.

Had equipment to die for back then (Hammond, Hohner, Vox, Farfisa, Moog and EML synths), but sold it off to pay for college. 

Another thought on the topic.  You hear basses go down to their low E-string literally all the time, so people have a feel for it (did someone say reference?).

But how often you you hear a piano playing low A?

After seeing Dick Contino I took up the Accordion. By the fifth grade the Clarinet was the only instrument open. I simply didn't practice enough and got the boot. Devastating at that age. Meh...

When I got to High school Paul Jackson soon to be Herbie's Bassist on Head Hunters was playing upright in the school combo. Why he took the time to introduce a freshman / surfer to the Bass took me a while to understand. He later mentioned quarter notes were the first notes I played without any coaching. Sweet man.

B3? My aching back. 

As to the Doors, I would hope that one's system allows them to differentiate the sound of a bass guitar...,

https://youtu.be/ptA39Awo0FE

and a Rhodes Piano bass...,

https://youtu.be/nOJSmXSFCWk

It should also be obvious as to whether Ray is playing a Hammond, a Vox, or a Gibson organ in each cut.

Piano bass limited in bass energy and duration and thus limited to be used in evaluation.  However, if piano bass is individually important, no reason for that particular person to not target piano bass excellence.

Also, bass preferences can differ - some seek bass energy, while others target better fidelity

The late great Oscar Peterson was gifted a Bosendorfer late in life and he used that low register a lot.  If you can find recordings by Telarc you might hear it.  Also the series "Exclusively For My Friends" originally recorded on BASF in the Black Forest has him playing on a Bosendorfer that I believe has those low notes.   There is also a great recording by Ahmad Jamal entitled "Ballades" on Harcourt of Paris that captures the full scale of the piano magnificently.