I know most of you feel like "just grab a burger and call it good" but it just isn't possible
Because it's all but impossible to get a kid's meal with a burger, either for CS or TS.

You mentioned Teppanyaki - their kid's options are Shichi-Go-San - Chicken or shrimp with grilled fresh vegetables, steamed rice and child dessert and Donald's Favorite - Grilled Chicken breast with mixed vegetables and steamed rice.
I suspect that once you start looking, rather than speculating, you'll be pleasantly surprised. Or you'll decide that the DDP isn't a good deal for you - no soda isn't a problem (my DD won't go near soda and dislikes most juice, so got water or milk at every meal), limited sugar isn't a problem (fruit cup or skip dessert entirely), fruits / veggies with meals isn't a problem (options for at least one and generally both exist) - but CS is by definition "fast food," and if you're categorically opposed to that, OOP might be cheaper for you.
IMHO, DDP isn't intended to be flexible; it's intended to keep people on-property. And it isn't intended to work for everyone.