I’m curious whether this old news to folks.
I happened to be listnening to music with an-old style set of headphones – the kind that cover the entire ears. After a tune, I happened to pick up my flute to play a bit. I happened to forget that I had my headphones on. WOW! The sound of the flute was very different (for the better). Very interesting variation on practicing.
John
https://forums.chiffandfipple.com/t/improve-your-playing-listen-to-yourself/48639/6
I know you’re not talking about using a microphone here, just the headphones to muffle the sound. Which is a mixed blessing. It does help to objectify your sound to a degree, and maybe gives you some idea of how your tone blends in a group setting when the subtleties are buried in the mix. Earplugs can give the same effect, of course. OTOH, you’re also masking flaws, which is a false improvement. OTOH (yes, I have 3 hands), anything that adds variety and interest to your practice isn’t all bad.
I hope over-the-ear headphones are not old fashioned! Real men don’t use earbuds. 
And a nice over-the-ear set like AKG 240s are standard kit for professional studio use.
I am currently dealing with an ear infection in one ear. It’s kind of like having that ear underwater. Although I’m not having this problem this time, in the past, I have heard two different pitches, one pitch from the non-infected ear and another pitch from the infected ear.
The sound of the flute was …for the better.
Earphones, eh? Get heavier ones! You might think it was better if you couldn’t hear yourself at all!!