This is a critical aspect of crossovers- since they contain the same signal, any phase differences between the intersecting components are easy to pick up by the ear and very difficult to measure since it won't show up as a significant frequency or amplitude differential. In the highly acoustically sensitive area where the crossover occurs, the phase distortion between the two signals is hard to pin down but it's definitely there, it's easy to hear by A/Bing.
I mix on a multiple-monitor setup and the one that is most critical to me sounds like absolute garbage. However, it has a wonderfully "flat" response and allows you to get an idea of what proven aesthetically-unpleasing issues are present. It has no crossover. The goal is not to have perceived rumble, tinniness, or mud on any of the incredibly wide range of listening systems out there. I think this is what beat means by "musical"- flat speakers are actually not pleasant to the ears, but the most empirically useful.
The most famous secret of many respected mix engineers is the Auratone. Michael Jackson's "Bad" was mostly mixed on this little thing. It sounds like absolute garbage aesthetically but reveals more issues in a mix than anything else. It's like when you first saw things under a "blacklight" as a kid and got to see all the particulate matter covering everything, that you can't see with the naked eye.
Here's more about the Auratone. I hope my comment has helped to bridge this critical area of "musicality" vs. empiricism. http://www.trustmeimascientist.com/2012/02/06/auratone-avant...
Postscript- the listening environment is the most important aspect! Always! You can have the best mastering grade monitors on earth in an improperly treated room, and it's all for naught!