Erik,
Some people are not at all sensitive to sound being out of phase ( as you describe ). Consider the case of the entire Polk Audio SDA line of speakers. The "speaker interconnect" tied one side of each speaker's midbass/midrange drivers to the other speakers matching drivers 90 degrees out of phase. The result was a wider more "encompassing" stereo image ( at least that was the hype ). I am so sensitive to phase that the SDA line literally gives me a head ache. I can walk into a room and hear a pair of speakers out of phase in under 2 notes. Every time. While working on the floor of an audio shop for 10 years and now running my own store I have had several instances of mistakenly wiring a speaker out of phase with the system and had customers expound on the fantastic sound quality. Each time I swapped things back to correct phase and about 1/2 of the time the listener either heard no difference or in fact preferred the out of phase connection. Not a scientific evaluation for sure but it has happened many times over a 20 year span with a lot if different people. Just my own experiences.
Some people are not at all sensitive to sound being out of phase ( as you describe ). Consider the case of the entire Polk Audio SDA line of speakers. The "speaker interconnect" tied one side of each speaker's midbass/midrange drivers to the other speakers matching drivers 90 degrees out of phase. The result was a wider more "encompassing" stereo image ( at least that was the hype ). I am so sensitive to phase that the SDA line literally gives me a head ache. I can walk into a room and hear a pair of speakers out of phase in under 2 notes. Every time. While working on the floor of an audio shop for 10 years and now running my own store I have had several instances of mistakenly wiring a speaker out of phase with the system and had customers expound on the fantastic sound quality. Each time I swapped things back to correct phase and about 1/2 of the time the listener either heard no difference or in fact preferred the out of phase connection. Not a scientific evaluation for sure but it has happened many times over a 20 year span with a lot if different people. Just my own experiences.