I have four adult children, and we played food-as-airplane with all of them. While it's true that they all lost weight upon entering college as they struggled with learning to feed themselves without our entertainment, I can say that they have all achieved normal weight and are adept at self-feeding now.
OK, that was an attempt at a joke. :-)
Play airplane if you and she like it. It's fun for the toddler, and if it gives you some peace about getting something nutritious into her, then it's doubly rewarding. All children grow out of this stage some time. Normal children grow up healthy in the presence of nutritious foods, even if they are not eating as parents think they should. Make sure there are lots of healthy options around the house, and not much sugar or junk food. If you're really worried, talk to her doctor about a daily vitamin supplement.
It's important to model good eating habits and to avoid food battles. I've added a link below that, if you can overlook the constant use of the words food neophobia, has some valuable advice about stages picky eaters go through, why they are picky eaters, and what to do about it. While I doubt your child is a picky eater, it just explains the phenomena pretty well (if it is a bit dense) and has some tips that anyone can use to get kids to eat healthily.
One last anecdote. I knew a child who had extreme tactile defensiveness, and would only eat (I kid you not, it was very strange) plain cheese pizza, chicken, pretzels, spaghetti/lasagna, peanut butter and jelly sandwiches, and raw carrots. Nothing green ever entered his mouth, no fruit or other vegetable, nothing but those foods, vitamins, and lots of fluids (low fiber meant lots of fluids). He also had problems in other areas (clothing, unfamiliar surroundings, weather sensitivities, etc.) He had the perfect parents, God bless him. They just fed him what he would eat without making a fuss. They accepted him and loved him as he was. Believe it or not, he was not sickly, obese, or detectably malnourished. He was very intelligent, unfailingly polite, athletic (not school sports, though), and grew into a fine young man who married, makes a living, and now feeds his own children. You may think that's not possible (I would not have believed it myself if I had not followed him for over a decade).*
In other words, it all turned out well in the end. He's eating better now as an adult. But I believe a saving grace in this child's life was having parents that just didn't make him feel bad about himself, either at the dinner table or away from it.
* Nothing worked for this child, not dietitians or occupational therapy, or psychologists. The parents threw up their hands in defeat, and made the best of it.
Food neophobia and ‘picky/fussy’ eating in children: A review