Ordinary hardware store washers might flex when you tighten the bearings into place and I'm not certain you would get the bearings firmly seated in the wheel?
Perhaps you would, but if they are a few thou away from being seated then the balls will be sideloaded when you tighten the assembly, and that will wear them fast.
But, since you said you got xx,xxx thousand miles out of the last set, I guess it's working OK.
At least with the gentle hammer and race method, when the bearings seat, the change in the "ring" lets you know 100% that they are seated ALL the way. In my experience, of course.
YMMV.