Also, letting your children only eat the foods they want to makes them far more susceptible to food allergies later in life. Children, especially young children should be exposed to the largest variety of foods you can think up to develop healthy immune system responses to them while the system is still developing.
Edit for Sauce:
It was a study done over 180,000 children in 51 different countries in 2012. One of the big things concluded was that eating a diet primarily consisting on heavily processed food 3+ times a week increased the chances of a child developing a food allergy or asthma by 39% over baseline. Conversely eating a diet containing a larger variety of unprocessed foods reduced this chance by 11% over baseline. With that study and others since the current theory is that the chance of developing a food allergy is directly relational to the food you are exposed to as a developing child.
RE: Food neophobia, an eating behaviour trait in which a person refuses to taste and eat new food they are not familiar with, may lead to poorer dietary quality and increase the risk of developing lifestyle diseases, finds a new study (n = 4,091, ages 18-83).