Cannot find perfect sound

Can't compare speakers to headphones--headphones are a pain in the ass to use all the time but for critical listening I put on my Sennheiser HD600's. Best I can afford but they are not influenced by room as most all speakers are.  What I like about speakers is good soundstage and dynamics and to hell with accuracy. Back in the day when I went to live concerts I was disappointed in the live performances because they lacked the subleties of studio recordings--not always but sometimes not to mention the wall of sound at about the threshold of pain. My ears were never the same after a Santana concert and I can't even imagine wanting to see AC-DC live.

If the problem is with timing accuracy, you may want to try out some DSP solutions that address timing as a function of frequency reproduction. Devialet's Speaker Active Matching (SAM) does that. So does Dirac Live Room Correction Suite (which covers the entire chain, including the room). Of course the room should be acoustically friendly.

Some people do not like the result, but on balance I've found that people are extremely pleased when they first hear the improvements possible.

You may also find the Stereophile step response measurements helpful. You can compare the Kef Blade Two to B&W, Revel, Vivid, etc.

for example multiple sets of speakers aka resonators, Linn knew this back in the 80s

This myth was debunked back in the 80s with Ivor as the listener: "The second test, also single-blind, used a Linn "Kan" loudspeaker as the undriven transducer. Again the female vocalist was used as source material. The loudspeaker lay on the thickly-carpeted floor behind the listening couch. It was placed either on its side (the "uncovered" condition) or on its face (the "covered" condition) according to a random series of choices. Ten trials were conducted during which Tiefenbrun achieved a score of 5 correct out of 10. Again, this demonstrates no discrimination ability beyond what one would expect purely on the basis of chance." from  https://www.bostonaudiosociety.org/bas_speaker/abx_testing2.htm

@kenjit What you are hearing is phase error. Vertical baffle speakers are the worst offenders. Since you are particularly sensitive, look at speakers with minimum phase error. Vandersteen and Wilson are a two that attend to this very real defect.

Most manufacturers ignore the issue. Most dealers, reviewers and the overwhelmingly vast majority of 'audiophiles' have no clue what you are talking about. They have also never heard what is on the recording!

It's not the frequency. It's the Time!

BTW, are you a musician?

You have a couple of choices and all are time and phase coherent designs. This is the key as why you like that sound.

Meadowlark - preowned.

Thiel - preowned only these days unless Tom Thiel (please!!!) can find a way to restart the REAL Thiel.

Vandersteen - NEW or preowned. (recommended even though I am a big Thiel fan)

Dunlavy - preowned.

Wilson DOES NOT DO THAT but instead inverts the polarity of the mid drivers so as to minimize the phase distortion caused by high order crossovers. From Stereophile for the Sophia:

"The initial up/down spike is the tweeter output; the negative-going decay of the tweeter's step blends smoothly into the midrange unit's step response, the positive-going decay of which blends smoothly into the start of the woofer's step response. (The tweeter and woofer are connected in positive acoustic polarity, the midrange unit in inverted polarity.)"
Read more at https://www.stereophile.com/content/wilson-audio-sophia-series-3-loudspeaker-measurements#eASZCHpoiE...

And it's not just this model but other Wilson models too.

Based on you description of what you like about headphones and your disppointment with the speakers you’ve listened to, these are your choices.