What would your "perfect speaker" sound like.

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...

I’ve already got The Room. Have lived here for more than 25 years. I bought the house simply to have the room. For my stereo.

The speaker is like the hand is to the amp’s forearm. They work together exactly like that. The ’power of the hand’ is the forearm. The work of the hand is the work of the forearm. The hand is the realisation of the forearm. Without the hand the forearm cannot acheive anything.

A speaker conveys the quality or lack thereof of the prior components. Before I acquired my perfect speaker, I personally would want to already have in place an extremely capable Source, Line stage and Power amps. If I had that in place and they were all very capable components then I simply want the speakers to faithfully ably convey the excellence of what came before them in the signal chain. What comes before them being chosen because they ably get to the heart of the musical message whilst simultaneously being technically impeccible.