Without this crosstalk, it's what the producers of the music intended. So, even if crosstalk improves it...should we advocate to music producers to add crosstalk? I don't think so—they produce the sound they want to convey in the studio, I think they'd want to maintain that authority. At best, if you're a person who like increased crosstalk, then I suppose it might be one reason you're attracted to it. (I wonder if there is a market for crosstalk boxes to add this feature to a digital listening environment, or amps/preamps or even DACs with this feature, in order to win back people from vinyl?)
Actually there is a market for crosstalk DSP which are mostly available as VST plugins. If you have playback software capable of hosting VST plugins (e.g. JRiver) some of them are free to try. Most of these plugins are for headphone users, but they also have an effect on your home system. As for a DAC with this feature, there is the RME ADI2 FS. In a home system there is already crosstalk from the speakers and you can adjust the crosstalk by moving and angling the speakers. Adding crosstalk upstream to the speakers seems to have a subtle effect on my system but the result subjectively seems to focus the soundstage more towards the center and reduce the width.
Yes, I've had Nx, then CLA Nx (better), for years. It depends on the mix of the source material whether it's an improvement, a detriment, or just different. It's especially good for mixes that have significant hard left/right elements that depend on the channels mixing in the air to sound right. For instance, Dire Straits' You and Your Friend sounds wrong on headphones, but with the virtualization it's sounds awesome. But, there is a lot more than just crosstalk going on. Anyway, my comments were specific to "what the producers of the music intended", as I noted. Obviously, it's unlikely that those responsible for You and Your Friend feel they made some mistake that needed fixing—even if I like it better with virtualization when listening with headphones.
And there's the other thing—you can't switch off the added crosstalk of vinyl playback. And not everything improves with it, though I don't think it does much damage.
Also, "that to some engineers is too unnatural", how many is "some"? Audio engineers work almost exclusively in digital audio, and I don't think many of them struggle with it due to sounding unnatural. Most talk about how incredibly good their premium converters sound. And if it's the difference between premium and typical, they both would be using linear phase most often, so I doubt it's "minimum phase" that's the secret.
Don't know. The experiment is easy enough to replicate provided you have access to an audio system like mine, where the crossovers are generated in a PC and hosted in a convolution engine. It would take me an hour to make a minimum phase filter instead of the linear phase that I am currently using. TBH I never did do that experiment to hear the difference between minimum and linear phase, I just read that linear is superior, implemented it, and that was that. I should go and set it up and hear for myself what difference there is. To be fair, linear phase does have its issues and not just with "unnatural digital sound". You need more computing power (which brings its own problems with expense, cooling, and fan noise), and you have pre-ringing.
"You need more computing power": But that's like saying a car needs more power if you have three bags of groceries in the trunk instead of two—while true, the car already has enough power, nothing really changes. High order IIR filters also require a lot of computing power, and luckily FIRs have pretty good efficiency near half the sample rate, a special case that is a huge win (it would be a different story for filters of arbitrary cutoff frequencies, particularly very low ones). Any modern DSP (or via FPGA) has more than enough horsepower for either, with no change in cooling (my DX7 Pro has no fan, has choices of linear or minimum phase, and it's just above room temperature to the touch). And if you really want to go insane with filtering (super long FIRs), to appease audiophile sensibilities, you can move to the frequency domain. Convolution reverbs are just insanely long filters.
Pre-ringing: I have serious doubts about this being a real problem. It may be, I've done no scientifically rigorous testing, I just doubt it. First of all, you need significant energy at the filter cutoff to get significant ringing, where music typically has less energy (yes, I understand we'd probably want to pay most attention to transients), AND the ringing will be at the cutoff frequency. I'm not going to hear it, maybe teens can, but on top of that it will be occurring while music is playing. I know how audiophiles like to say they can—or at least suspect they might be able to—sense things that are unnatural even if they can't outright pass a test proving they can hear it, but I'm just saying that I personally doubt the pre-ringing issue is a problem. Of course, with minimum phase, you get post-ringing, and more of it. If any of that is really a problem, it would be hard to argue it's still a problem with higher sample rates. (I'm not saying we must have the higher sample rates, but, for instance, does 96k shut people up who feel that digital sounds unnatural? Not all of them, certainly.)