Most people want roll-off, it's been thoroughly tested. I even remember a DAC that had that same roll-off slope built-in, lol. That's how we hear live music (as well as other sounds) in real life because high frequencies are attenuated over distance moreso vs lower frequencies. So with a stereo system we sit close relative to a concert and if you have a flat response it seems unnaturally tipped-up... because IT IS. So we want some roll off.
On coherence, I've found it varies a lot more from person to person. Some people aren't sensitive to a tweeter sounding disjointed, others pick up on it... I have tested this, the people who picked out the issue were invited back later to comment on further iterations.
Same with extension, some really notice it, other not so much. My T500s go up pretty high and I can hear an 18 kHz tone still, so for me I prefer the tweeter, but only after putting some effort into figuring out how to make it coherent. The speaker sounds great with the mid run w/o lowpass and no tweeter, the response is just less even than ideal over 15 kHz but you still get the psychoacoustic effect of highs being present. If you change to using an xo and tweeter, some people can hear the tweeter is more accurate and appreciate it, but it's at a frequency many people simply can't hear clearly anymore. For that reason, my speaker will give you the option to use it or not. If you're super-sensitive to coherence and can't hear over 12 kHz anyways, you may not want a super tweeter.
It doesn't seem like something Peter would be into...
