I prefer thru axle - but have two older QR / disc brake bikes and they are fine. As others mentioned - ensure QR is properly / sufficiently tightened.
I often transport bikes with front wheel removed (as shown below). One bike with QR / disc brakes will sometimes have slight rotor rub after the front wheel is re-installed. ( The other bike never has this issue ). If this happens, I will loosen the QR, rotate the axle (cone) 1/4 turn and then tighten the QR. A quick spin of the front wheel will then reveal if the rotor rub is gone - sometimes another 1/4 turn is required. This has worked every time.
How do you have your bikes secured to the floor?