Or pry the door frame apart and tap it back in place after rolling the rack out.

Worth a mention as many door frames are easier to remove than a number of people might suspect .. fewer pieces to disassemble than many {object}'s and not an uncommon hack when moving furniture.

Removing door frames is easy. Putting it back together without looking like crap is the hard part.

Repeat after me: caulk and paint make it what it ain't

It's "caulk and paint make me the carpenter I ain't"

For the one I have that would be irreversible. You‘d have to cut it up.

when i moved to this apartment, the wooden wardrobe i had in previous one (built on the spot) could eventually move through that door and corners but absolutely could not move through this doors/corridors/corners (or staircase). So.. i got a power-jigsaw and cut it into upper and lower halves. Those moved easily. Then "assembled" them halves with lots of metal planks and screws on the new spot. Tadaa...

Luckily it was wooden.