You may want to double check that definition. A balanced diet contained an adequate and not excessive supply of all the nutrients a human needs to survive and be healthy. It doesn't matter where these nutrients come from. They could be all mixed together in an artificial tasteless brick for all it matters.
Your digestive system probably wouldn't like you very much if you did that though.
Do you know what the different types of protein are, and sources for all of them? If you did you'd know that there's vegetable sources for all of them. Please, read a book on nutrition, even an introductory one. You'll learn so much.
I'm an engineer, not a doctor, but I still know the shortcomings of a vegetarian diet. I also realize how stupid and hypocritical it is to adopt such a diet for "moral" reasons.
Because I'd remember my previous lives.
On a more serious note, I simply don't put a whole bunch of stock into something that can't be proven and that I don't find very compelling. In other words, I put more stock in UFOs and aliens than reincarnation, but that's mainly because UFOs and aliens actually have more evidence supporting them, and frankly they're more interesting than religion of any kind.