well, traveled many times with a garment bag even on domestic flights in France

when all compartments are 200% full, you can just ask FA to put it somewhere flat


anyway, most luggages when not lost are delivered within the next day in 99% cases, therefore emergency items (toothpaste, toothbrush, tshirt) are just enough for a night, considering that you would take a shower, put back your clothes until your bag is delivered

there is no reason to treat top tier and other passengers a different way, same as when a flight is delayed or cancelled


moreover top tier cardholders usually travel with premium credit cards with insurance covering the purchase of emergency items, they don't have to rely on oversize tshirts