The plan doesn't work for us either. Since we are
DVC, we no longer get the free dining plan, and would have to pay if we ever wanted it. Then, it definitely doesn't work for us.
Mind you, free isn't even free these days where the dining plan is considered. It used to be you could get the normal plan (1xTS, 1xCS, 1xS) when staying at a value - now you have to be at a deluxe resort to get it, which involves paying extra compared to a value! lol. I guess if you were always going to stay at a deluxe, then free dining is a blessing. If not, then it really does require some thinking.
Anyway, back to the question at hand. The first time we did the dining plan, we pretty much managed to use up all the credits we had, but it was the first time and bit of a novelty. Plus, there were a lot more things that counted as snacks! Second time around, we used up all the TSs and most of the CSs, but hardly any snacks. Ended up buying boxes of cookies to take back as gifts.
The holiday before last we did a split stay as DVC, so paid OOP the first week for food, and paid for the dining plan for our second week, mainly to see if it would be worth it in the future. I would say we probably spent a little more the week of the DDP.
We ate more the second week than we did the first. The first week, we most of the CS, we'd get two and share them between three, and we rarely had any snacks. Second week we always used the three CSs, although we still had loads left over, and once again we didn't use many of the snacks.
For us, we tend to eat breakfast buffet TSs, and not a lot of CSs or Snacks, so there's no real value in the DDP for us. I think it's a very personal, family thing and depends incredibly on what you are and are not likely to eat and how you'll go about it.
There are plenty of menus on the Dining section of this site with prices, so it might be worth going through those, seeing what you may and may not eat, and working out at least quickly how much it might be if you paid OOP?