By fostering the development of a vibrant third-party marketplace for adventures and other tertiary products, WotC reaped increased sales of its core rulebooks, driving revenue above where it would have been without an OGL. The reason is that a vastly expanded universe of low-margin adventure products create demand for the core books, which provide the bulk of WotC's D&D-related profits. Further driving 3e sales was the protection against forced obsolescence that 3e rulebook purchasers enjoyed under the OGL, because anybody who was on the fence about purchasing the core books knew and understood that their edition would continue to receive third-party support in the event a substandard new edition was eventually foisted upon them.
In theory. Unfortunately, you're comparing the real-world results to a hypothetical, which is always dicey. We don't actually know how 3e would have done without the 3rd party publishers, or, say, with a license that gave WotC some say in quality control.
It is a plausible argument, but there are enough variables that plausible does not equate to a sure thing.