Is there measurement that correlates with cohesive/pinpoint imaging?

AFAIK, there is no 1 number for this, but if you want to jump into a fun rabbit hole, research "Head Related Transfer Functions" or HTRF for short. :)

Is there a measurement that correlates with sound stage depth? Width? Timbre? Palpable presence? Slam, punch, drive, grain, glare, detail? Is there a speaker measurement that actually does correlate with anything that matters? Yes: sensitivity. 

Does it tell you anything about how the speaker sounds? Not really. But at least it does give some idea how much power you will need. Which is more than can be said for any of the other measurements. 

Its the only measurement I paid any attention to when buying any of mine.

Well, that's unfortunate!  Lots of speaker companies claim to have a focus on coherent imaging, but nobody has any idea how to measure it?  Do phase alignment/time alignment correlate?

Lots of speaker companies claim to have a focus on coherent imaging, but nobody has any idea how to measure it?

it is measured by frequency response tests

Hey OP:

You really should at least start to read about HRTF. It will help you see the problem of imaging in a whole new light, and why it is so hard to measure.

  Do phase alignment/time alignment correlate?

Not in my experience, but clearly the fans of speaker brands like Thiel and Vandersteen feel strongly they offer special features you cannot achieve otherwise.  Personally I vote with the literature, that says we aren't that sensitive to phase or time alignment. We _are_ sensitive to badly matched drivers however.

There's also some research saying that making the frequency response dip around 2.4 kHz enhances the experience with the trad off being a neutral frequency response.

It is also important to include the room in these discussions. Not only does controlling reflections matter but enhancing diffusion in areas also helps a great deal.  I find that imaging is enhanced in the same plane as the room treatment.  Want wider?  Treat the sides.  Want taller?  Treat the ceiling.  Want depth? Treat behind the speaker and behind the listener.

The best speaker in the world can be ruined by a poor room.  Conversely, some speakers reduce the interaction with the room, like line sources, planars, horns and open baffle.