Nearly all manufacturers do not advertise/exhibit their product measurements? Why?

Manufacturers (or, more accurately, designers) measure certain parameters of their gear as part of the design process, and then they listen and voice the product to achieve the final result. Selected measurements are used to develop the product specifications, which are summarized in the published manual. I suspect most manufacturers believe the product specifications provide sufficient information about the product performance so that buyers can make an informed purchase decision. If they believed it would help sell the product, then they would probably provide a full set of performance measurements. As you implied, there are exceptions such as Lamm that provided measurements of each amp and preamp they sold, and there are others. There are also designers/manufacturers who take pride in achieving certain performance measurements, such as Cees Ruijtenberg at Sonnet Digital Audio (formerly Metrum Acoustics) [linearity plot from Sonnet’s Pasithea DAC/preamp].

I suspect raw product measurements are sometimes massaged before they are documented in the published specification, and that every single measurement used in the design process does not always make it into the specification. However, when preparing the published specs, the manufacturers probably don’t stray too far from actuality in the event that John Atkinson, Amir, or another entity or publication decides to actually measure the piece and publish the results alongside the published specs. My Aerial LR5 speakers were measured by Thomas J. Norton, and the measurements were published in a review by Michael Fremer.

As examples of why specs may vary somewhat from the raw measurements:

• Amplifier manufacturers like to show their amp’s power doubling when measured from 8 to 4 ohms, so they might take the power measurement at 4 ohms and divide the result by 2 to obtain the published power at 8 ohms, even though the actual power at 8 ohms may be greater than published,
• a preamp’s output impedance measurement may be reported as the single value measured at 1K ohms, instead of the range of values from 20 to 20K ohms, because potential customers may realize the higher output impedance values that sometimes occur in the lower frequencies would cause a low bass roll-off when used with a power amp having a low’ish input impedance, and
• speaker efficiencies and minimum impedances may be reported in a manner to maximize those performance parameters and thereby reduce the potential for lost sales to folks whose amplifiers are not powerful enough to drive low efficiencies or low impedances.

For an on-topic interview, Google "Why John Atkinson Believes Measurements Matter."

@carlsbad Yes, I was banned in less than 2 hours.  You can read about it on the Audio Science Review review on Audiogon.

@mitch2 The real problem are cables and tweaks.  Where are the electric and/or acoustic specifications (let alone measurements).   So much puffery and exaggerated promotion without a hint of specs or measurements, in general.

As to equipment, your examples of specs not conforming or relevant as measurements is also common.   So often power output at reduced impedances are lower and occasionally at 8 ohms lower than actual.  Impendence mismatches can be a problem.  I purchased Legacy Signature IIIs from a guy with a Boulder amp and some boutique tube (unknown) preamp.  They sounded quite awful which the seller admitted as the reason he was selling them.  I brought a Sherwood 7100 16 watt 1970s receiver.  It blew the seller away.   Great mid-fi sound, including decent bass.  He had already ordered other speakers so he let me buy the Sigs.  Legacy speakers post high efficiency but they have low impedances with occasional sharp phase angles.  While many decent 35 watt receivers can power them with good current/power supplies, other amps one would assume could power them (especially the bass) with 70 watts can't.  

I still think most manufacturers could do better.  Even the speaker company I want to buy my future speakers from has very limited specs (Von Schweikert).  

Cause it’s about the music man! Not the measurements. 

This reminds me of the Carver Corp. claim in the 80’s that their amps could replicate the sound of any other amp design by adjusting the “transfer function” which was Bob’s buzz word for frequency response plus noise/ distortion profile.  Unless I’m mistaken these amps are not regarded as belonging in audio Valhalla.  The idea that ASR can characterize how an amp will perform with speakers using their methodology is just as suspect today as when Julian Hirsch did it for Stereo Review.  But it is also hard to make the case that an amp that demonstrably alters the signal by its performance can somehow be more high fidelity than one that “measures well”. 
And who would believe manufacturer’s specs anyway?  Independent reviewers are needed for credibility. As long as their credibility is trusted. I trust John Atkinson in Stereophile more than Amir or the shills at Ab Sound.