I wouldn't use a full storm cover with straps unless the car was completely clean.
I do have one but it's rarely used for that reason. Overnight in windy conditions the straps are very likely to mark the paint.
Mostly I use a cockpit cover which doesn't contact the paint but keeps the hood dry (and the interior). I use the cockpit cover every day when touring.
Also take the bag for storing the wet cockpit cover while travelling.
