For paint to adhere, a surface needs to be free of organic debris and loose/peeling paint. If either of these are not visible to the naked eye, then there is no need to power wash. If only particular areas, such as eves or stem walls, are effected then a localized prep can be substituted for a full wash of the home. If a full rinse of the entire house is needed then a garden hose or low pressure power wash is used until the runoff water is clear. Let the stucco and trim dry completely before painting, usually 2 hours for water only and 1 day for solution cleaning.
You should only pay for what you need. Contractors charge for every hour they are on the job, so unnecessary work will cost you.
Note: Power washing can be dangerous if not performed properly. High pressure water can go through many surfaces almost instantly, especially if you are using a 3,000 psi pressure washer. You could conceivably carve a hole into the side of your house. In fact, highway crews actually use a version of a pressure washer to cut the holes for dynamite blasting when digging for highway construction.