Exactly... and that also makes sense to me

It is an IIR DSP, since when I jumped the active adventure more than 10 years ago, FIR was not available in 8 channels and with a low noise analog section.
Now, I have still not fully been convinced that FIR can offer a true audible difference - a technical and measurable - but audible?
Well, "is it audible" is kinda can of worms territory.
@BenB has already stated that phase may be audible in some frequency bands. Toole and Linkwitz would disagree with him. They think that intrachannel phase distortion is inaudible. There is something called "Ohm's Acoustic Law" which says that you can't hear it. However, there is
a discussion on ASR with JJ who unequivocally states that phase is audible, if the deviation is more than 15 deg per ERB and provided the ERB bands are next to each other. I made a post in that thread where I looked at several studies cited by Toole, and showed that they studies were done by adding phase distortion on minimum-phase speakers. In other words, time smear already existed in the loudspeaker - what if we time smear it even more. If you read Linkwitz's blog, that is exactly the same experiment that he did.
I use linear phase FIR's and I have conducted my own experiment comparing min phase vs. linear phase. I have gone so far as to straighten out the minimum-phase behaviour of my drivers and make them linear phase. In my opinion, it is
easily audible. The difference is that the lin phase version has so much more clarity.
The problem with my opinion is that it is anecdotal, and there are no published studies that support it. I begged JJ to publish, but he said that he does private work now and no longer publishes. Regardless, he has several test tones in that thread that you can download and try. Decide for yourself if you can hear a difference.
BTW, there is an additional consideration - I also believe that placing the MLP within the critical distance is important if you want to benefit the most from lack of phase distortion. Again, this opinion is my own and it is anecdotal, although I came to this realisation by reading Griesinger's writings on proximity. He said that the sensation of "proximity" is created by loss of phase coherence due to contamination by reflections the further you travel from the sound source.
So right now my opinion is admittedly on shaky ground. I believe lin phase sounds superior, but without any publications and with people like Toole and Linkwitz saying the opposite, I realise that I have little persuasive power.
And which gear actually exist, where you can switch smoothly between IIR and FIR with the same setup, speakers, amps and room, where the absolute only difference is the phase-correction?
Any PC based convolver can easily do it. Create minimum phase and linear phase versions of the filter, then load it into a convolver. The best convolver for this kind of testing is
Hang Loose Convolver since it is zero latency.
When using my system from both gaming, movies, tv, and youtube... then I would deny FIR any day, if there's just a hint of delay, so that lip-sync is a problem - I just can't live with the unnatural experience when there's a timing difference between sound and picture
Well, that is a problem. The solution would be to use FIR for music, and IIR for video. The issue is that switching from FIR to IIR is not a seamless experience for my wife. It is easy enough for me, but it isn't for her. In fact the whole PC based setup is so complex that she can't use it. That is a major downside. I have enough brains to make it work, but not enough brains to make it usable.