Try measuring the crossovers. Many of them are higher than 1st order despite the claims. 1st order crossovers are rarely a good idea when designing a speaker to produce high output levels with minimum distortion and compression.
I must say, I have also never seen any worthy proof that a speaker with a first order crossover exists. And let's make something clear here, we are not talking about electrical 6dB, we are talking about a speaker which hits true 6dB acoustical slopes. Would sure love to hear one!
It has been blind tested many times, shallower slopes do indeed sound better. But... 6dB is impossible. And 12dB is extremely hard to pull off.
First, 99.99999% of all drivers are manufactured in a way that they literally design themselves into LR 24dB slopes with 2 parts in the crossover. Using a slightly asymmetrical (shallower on the woofer) LR4, one can easily design a nearly perfect speaker, which is time aligned and minimum phase. The system should have lower distortion because of the steep slopes and better power handling. Drawback = group delay.
So, since shallower slopes tend to sound better, how to design them? Out of hundreds of drivers, there might be a handful which can be used. Shallower slopes = higher distortion and lower power handling. Let's say the system will never be pushed hard... With shallower slopes, it is impossible to time align a speaker using asymmetrical slopes. A.) The baffle has to be severely slanted, which causes other problems as now one will be listening to ALL drivers off-axis. B.) Do an ugly, expensive, and inconvenient modular design, where the tweeter can be physically offset from the midrange/midwoofer. C.) Use a lattice network to delay the tweeter. A lattice network (check out Dynaudio) is extremely complex and adds the same amount of group delay as an LR4 filter, negating most of the benefits LR2 had to begin with.
Forget about designing a 12dB crossover. But there is a place where one can hear what it sounds like. Seek out the very expensive Dynaudio speakers. The most expensive Focus and up mostly use 12dB acoustical slopes with lattice networks. The Esotar tweeters and midwoofers are absolutely state of the art and are specifically designed to work with shallower slopes. The speakers mostly sound terrific, but Dynaudio is only one of few companies in the world who can hit 12dB acoustical slopes.
Every company brought up and discussed here uses LR4. They include: Revel, TAD, Infinity, JBL, Klipsch, NHT, Paradigm, B&W, Magico, YG, Goldmund, Polk Audio, PSB, Axiom, Aperion, RBH, Ascend, Salk, Philharmonic, Focal, etc.
Dynaudio is the only company that I know who makes LR2.
Thiel and Vandesteen is one giant question mark. They for sure don't hit 6dB acoustical slopes. The slopes are shallower than a tradition LR4, but it's a mess if you ask me. Thiel has a slanted baffle (off-axis problems galore). Vandersteen physically offsets the tweeter, but the speakers measure bizarre...