Anybody own a component that sounds better with the cover off?

Not this week.

Yes; the Eastern Electric Minimax DACs that I have sound better with the covers off, because I have rolled into them discrete opamps. 

TT cover on/off———no difference. 

Change cartridge, ...adjust weight..... cover off/on - cartridges sound same with cover on or off,
I leave them on for convenience, and to keep in good shape, when things come off, get stored, scratches, cracks magically appear (PFM)

Hello,
I just took the dust cover off my Linn Axis. It sounds better with it off. I think everything matters. You just have to decide how much. Is the juice worth the squeeze? On my system the answer is usually yes. I do agree with the storing of products. Things can get damaged. Also the costs to improve the sound. The costs of isolation products can really add up.  I have petrified wood bookends on some of my phono preamp, BlueSound Node 2i, and the to of my amp. They can handle the heat, definitely improved the sound, and they look good. 

If you really want some bizarre reading go to Mapleshade Audio and read his suggestions for good sound. One of them is never run gear with the covers on. Some of his stuff is out there but a lot of it works you have to let your ears decide.