In our house, we have a 8 yr old daughter who loves vegetables (absolutely froths over Brussels sprouts and broccoli...weirdo) and our 5 yr old boy has Coeliac disease, which rules out gluten...he is a very fussy eater, it borders on painful watching / trying to get him to eat
But what we have found is we got the kids in the kitchen and made some healthy options, including treats. They love making food, the process of seeing something come together has really engaged them and they are super helpful and enjoy the whole process now, it does mean we spend a lot of time in the kitchen but its been worth it, the daughter never asks for take away, at 8 yrs old she has never has asked for it, probably because shes seen friends have it, but she doesn't become negative about being told no, instead we make our own versions at home, shes also never had soft drink.
The son doesn't ask for take away as he knows being a coeliac means its just not safe for him and again we offer to make safe and healthy versions for him.
I understand getting the takeaway is just easy, hassle free etc, but we made the call to not implement in our kids diets and yes it does cost us time but its something we are happy to do.
My kids also get teased at school because of the "yuk" looking foods they have, but my daughter is incredible about it, she just carries on and tells the kids that its healthy, that she made it and is not processed and full of things you dont need.