Exactly. Swap kills the card. But even if you turn the swap off (in linux or windows) I think these systems still write more often than amiga-like systems.
BTW: Do I have to 'shut down' MorphOS before I turn the computer off or just push the power button like I do in Aros?
A card (or even better, a SSD disk) nowadays usually comes with sector management which should help even against swap - but why would you use swap on such systems in first place? Buy enough RAM and forget about swap.
You can shut down immediately. Doing it from Ambient is usually faster than doing this via the power button though.
