Directly speaking in regards to acoustical slopes, the best I can do to explain my position is to describe what I'm hearing. To me, LR4s sound unnatural, flat, dead, lifeless, small soundstage, impossible integration between the tweeter and the woofer, harsh, tizzy, etc. This maybe another reason why I've never like ribbon tweeters. All of those designs use LR4s. As a matter of fact, I'm having a hard time thinking of a speaker that I truly liked which used LR4.
The new B&W lines (CM, Diamond) use first order electrical filters, roughly second order acoustic. Same goes for most Dynaudio speakers starting with the Focus line. Vintage Thiels (i.e. CS 3.6) were close to first order acoustic. Not sure about the current Focal lines. The legendary Goldmund Dialogues/Meta used elliptical filters. Ensemble PA-1, another classic, was also LR2. Some of my favorite kits like the Zaph ZD5, Excite Audio, and many designs from Troels Gravensen are mostly second order acoustic. That pretty much covers 95% of my favorite speakers.
I'm starting to believe that LR2 is the holy grail. But higher order filters like the eliptical/cauer also sound good. It just leaves the LR4 as the only topology which produces terrible sound.
LR4 requires the least amount of knowledge to design and the lowest cost to produce. I get that. But I wish more manufacturers used LR2 and hired better engineers for both speaker driver design and crossover design. It's not THAT difficult.