Exactly, the Founders are nothing if not elitist.
I don't think elitist
is the right word. In any event, the Founders clearly don't trust solids. They also believe it's their duty to impose their order on the galaxy. I refuse to believe they'd give up the control that's so important to them solely out of convenience. The Changelings are not a group of beings who take the easy way out.
I see what your saying. But as a counterpoint, consider that in the Gamma Quadrant they do have (their idea of) order. They pretty much own everything there. Most planets are subjects of The Dominion. They could have very little reservation with letting some poor beat-down subjugated race produce White for them there.
I could see the Founders getting a sense of smug amusement to see solids manufacturing a substance which they use to control other solids.
The problem of course would be the Alpha Quadrant production, since they have no such whipped races there, so as you said their last resort was to deal with the shady Son'a.
EDIT: I see as I was typing this R. Star made many of the same points, and a bit better than I did too