My eldest went through this, but when she would eat only one food, it was only one food. We could get her to drink milkshakes or the occasional yoghurt with her one food, but eating sandwiches and cereal along with her chosen food would have been a dream.
She was weaned on a wide variety of fresh, home-cooked foods, but at around 4 or 5, she just stopped eating. She would fixate on one random food. The only time it really worried anyone medically (she was under a specialist for eating/weight) was when she would fixate on something like plain boiled carrots or sliced cucumber, which she would have for breakfast, lunch, and dinner. If she couldn't have her food, she would eat nothing. A few people told me not to offer her her chosen food and that she would eat when she was hungry, but she never did. Even sweets and desserts were refused at times when she was fixating.
Advice at the time was to offer her her chosen food with something, e.g., carrots, mash, and chicken or cucumber and dip, but not to force the issue or make a fuss if she did/did not eat the extras. We were also advised that if she will eat it, let her, even if it's junk food. Vitamins are easier to supplement than fat, protien and calories.
She had nutritional supplements prescribed and attended play sessions around eating new foods, which were based on her cooking new textures/playing with food. The play sessions were very useful; she would often end up tasting something while she was playing/cooking, and it would sometimes be added to her list of food she would eat, even if just for a few days.
She grew out of it by secondary school and was later diagnosed as autistic. She's 22 now, she still has some minor issues, e.g foods cannot touch, certain foods cannot be on a plate with other foods, she needs a certain type of fork, but her overall diet is varied and fairly healthy.
I don't think anyone would have worried at all if she was eating the variety of foods mentioned in your OP.