Are first order crossovers best?

Blindjim, with all due respect You might be a bit off base with some though certainly not all of your assumptions. Many of these issues can and have been argued here ad nasuem. While I admire your approach, perhaps it might be best to just use your ears and determine what you seem to like and then determine if there seems to be any correlation or similarity between those systems/components. From there you might find a springboard into the archives and into the current and future forum to confirm your impressions and perhaps open your horizons to other gear that might fit into your personal preferential hieracrchy. Good luck.

Unsound...Where did you (and a lot of other guys)get the idea that a first order (6 dB/oct) crossover has no phase shift? Actually the woofer and tweeter phase varies with frequency, but always differs by 90 degrees. The tweeter can be physically positioned so that at some particular frequency, usually the X/O frequency, the two drivers are in phase. As you get away from the X/O frequency the phase difference between drivers becomes unimportant because one or the other is attenuated. Inverting the polarity of one driver changes the phase discrepancy from plus90 to minus 90...take your choice.

Polarity inversion makes more sense for a second order crossover, where the phase discrepancy is 180 degrees. The selling point for fourth order, apart from the 24dB slopes, is that, with 360 degrees of phase shift the drivers are in phase. Fourth order is difficult and expensive to implement with a passive speaker level X/O, but quite easy for an electronic line level crossover.

Correct you are.

And after listening to many different speakers in many different price ranges, Vandersteen speakers sound the most correct (realistic) in their respective price ranges, and even when compared to higher priced models. Geeze, did I piss away money before wising up!!!!!!

Beware the quicky listening tests at dealers!! Can you live with the speakers in your own home for years after the purchase? Why do you see SOOOO MANYYY speakers on this site for sale? I bet that most have a problem area with certain music in the living space that makes the owners want to "upgrade".
Just an idea...

Eldartford, just trying to keep it simple here. That's part of the reason I was suggesting that one has to consider a speaker as a system and that taking one parameter from the whole can be problematic.

For the people that haven't seen it.Here's a nice little walk through by Pat McGinty on Time Coherence and how to read a step response of a loudspeaker..The Step Response Reveals All.Of course time coherence is just one part as speaker design is quite complicated atleast for me.