The plans will save you money, IF you get a plan that is structured the way your family normally eats.
If you normally have a TS dinner every night and grab CS for lunch every day, the Basic plan will save that family money. The cost of a TS dinner (at Tutto Italia for eaxmple) alone pretty much equals the cost of the Basic dining plan. So for this family it's like getting the CS lunch and snack credit for free.
If like our family, you do a character/resort breakfast every morning, a few TS lunches, and about 5 signature dinners in an 8 day trip, the Deluxe dining plan is going to save our family money. It DOES save our family money. The cost of our dinner at Yachtsman and our breakfast at AKershous in a day (for example) is MORE $$ than the deluxe dining plan cost us for that day. Plus, we got 2 snack credits and a refillable mug, so yeah for us! We would order the same items whether we are on the plan or not. It is a plan that is structured perfectly to fit our families needs. Now for a family that would prefer to eat a CS breakfast and lunch every day, the deluxe plan is not going to save that family money.
In the case of the OP, a dining plan is probably not a good fit.
I have friends that do the deluxe plan as well, but eat some CS meals with it...something we would never do. I pointed out that they'd get a better bang for their buck if they did mostly TS meals and more signatures, but they don't care. What they like about the deluxe plan is that every meal is covered and paid for ahead of time. They eat whatever they want and don't think about it, like an all-inclusive. So for their family, it works. Even if it's not saving them as much as it saves our family.
Every family is different. We know a family that just went in Nov and they have 3 teenage boys. The DH booked the trip with
AAA as a surprise for the family. When he told DW that he just picked the regular dining plan she freaked out. She told him that those boys would cost them a fortune in extra food and how could he be so crazy to book a plan that only included 2 meals a day when their boys (all over 6 feet tall and skinny

) eat like 5 meals a day!! Needless to say he called the
travel agent and switched to the deluxe.