What would your "perfect speaker" sound like.

hertzhead

You might be a little to optimistic about what is possible or even what is desirable. Not sure how my listening room would respond to 10Hz or even 40Hz...

It might be possible to compensate with the calculated use of psychoactive drugs...legal of course ...but that is not my area of expertise....though it was for a while. 

You might be a little to optimistic about what is possible or even what is desirable. Not sure how my listening room would respond to 10Hz or even 40Hz...

Badly probably. That’s where Digital Signal Processing comes into its own.

For live music, the Eminent Technology LFT-8b.

For studio, the KEF Reference 1 Meta.

For over ears, Stax  SR-L700.
 

The best headphone sound like speakers timbre and out of the head spatial qualities...

Almost no headphone is good design.

But with the right DSP and right equalization, and control of resonance, and the right headphone acoustics design  (i know only one but some other must exist out of my budget possibilities) some headphone are like speakers at some level) ..

For speakers it is the link with the room and our ears/head location and measured state that matter ...

Headphone or speakers, it dont matter : timbre must be natural and sound spatial qualities must be evidently manifested...