First: Let us separate the OGL (which is a license) from the SRD (which is content).
When people publish material using the SRD base, it enhances the value of the D&D brand by increasing the value of the game to all the people who play it. The more "stuff" people have to use with D&D, the more likely they are to play D&D, start playing D&D, and talk friends into playing D&D.
Second, WotC benefits from the expanded pool of designers making content compatible with its own work. It can bring the best of that material into D&D, and it can hire the best of those designers and add them to its staff. Having a large pool of people who do work on the system also means that problems are identified faster, and solutions proposed and tested faster, than WotC could manage with just its own pool of designers.
Those are the overriding business reasons WotC licenses you to use the SRD content.
Your original question boils down to: "If WotC wants people to work on its system, and doesn't charge a fee, or have approval rights, why not just put the SRD in the public domain?"
There are many reasons. Here are a few:
1) Material "in the public domain" will rapidly become contaminated with work that should not be mixed into the "open" content by people who don't know any better (or who are grinding axes, or who are purposefully contaminating it for their own economic or political reasons). Pretty soon, anything you wanted to do with the SRD would become riskier than making new content from scratch, which would actually be a step backwards from the pre-OGL environment.
2) The OGL ensures that the creators of content get full credit, which you could not do with public domain content. Every contributor of new Open Game Content alters the Section 15 declaration, and that declaration gets used in all antecedent works, so the "chain" of creator credit is maintained. This may not seem like a big deal, but to many people, "credit" for their work is more important than compensation for doing the work in the first place.
3) The OGL allows a publisher to mix non-Open work with Open work freely. For example, I can write the statement "Darth Vader has 55 hit points" using the OGL, correctly using the Open Game Content (hit points), and limiting 3rd party use of the closed content (Darth Vader). Considering that a substantial portion of the RPG market consists of licensed IP, this is a huge point of differentiation, and is a key reason the OGL has succeeded. Without this ability, the SRD and the OGL would likely be limited curiosities, and not the market-shaping force they are.
4) The OGL equalizes the market. You can use it, but if you do, some of what you create may need to be freely licensed to other people too; the benefit you got (free content) is therefore transmitted to new users as well. This creates a positive feedback loop wherein everyone gets more and more value the longer the system remains in use. Individually, and in the short term, that may be a negative (you might want to limit other's use of your material to maximize your ability to earn money from it), but collectively, over the long term, it's a net positive (you may get back improvements in your own work you didn't even think about, and can incorporate those into future products with a higher value as a result).
Ryan