I'd be more inclined to agree with Nala, it's not
Free Dining nor the Dining Plans in general, but rather the root cause that brought both of those into being.
This is only conjecture on my part, I simply haven't been around long enough to know if this is the case, but it makes the most sense to me. Here's how I see the business logic:
0) Restaurants sitting (relatively) empty and dining profits are down.
1) Implement Dining Plans to get more diners into seats. Include everything with it
2) Tweak the new Dining Plans to improve table turn over (remove Apps), at the same time, remove tips to save some extra company money (and as the solution to a common guest complaint regarding servers who "just weren't trying").
3) Restaurants are filling up, but money still has to be saved, so this is where they'd start cutting the quality and quantity of selections. See what sells well and what doesn't. Cut the menus down to 5-6 solid choices rather than a dozen. This saves on ingredients, staff training, and overall time.
4) Start staffing cutbacks. (They've done this some, but I have a feeling that this is more the "next" step than the current one)
Now, again, I'm definitely not saying this is what happened, but it's what makes sense to me. Since we can see the DDP (as well as Free Dining) is incorporated before the Quality and Staffing cutbacks (and anecdotal evidence supports this), it's easy to blame them on the Dining Plans in general. My logic tells me that they are simply both symptoms of the original issue. This is supported by several non-DDP restaurants as well as restaurants in other areas of the country also trimming menus and/or quality. These places do not have the (or a) dining plan, and they're cutting costs the same way.
Of course, the dining plan does have its own set of issues (and one of them being the amount of reimbursement that the restaurants get). But, we also don't know both sides of the deal. Does Disney sell them ingredients on the cheap? Disney marketing is certainly part of the deal on Disney's side as well, which is proven by the raw number of people showing up for dining since the plans were introduced. I'm sure there are many facets to the whole contract.
However, with that said, I do agree that something needs to be done to stem the slide (perceived or real) sooner rather than later.