What a cutie your daughter is!
My oldest three granddaughters are allowed to have their hair any way they like; hair is a battle their mama has simply chosen not to fight. Letting bangs grow out is a hassle, but only for a few weeks. I believe I've seen some girls' hair clips/barrettes that are supposed to work for fine hair; your might check online.
If it's in your budget, you might take her to a hairdresser for trims so the hair will look better as it grows out. That hairdresser might have some good suggestions about how to take care of her longer hair. It's good to have a pro around now and then.
My long-haired grans - one has fine hair and the other two have thick hair - have major trouble with tangles, and they do use the spray detangler (they wash their hair about every other day so it can't make their hair icky). This summer I showed them how to braid their hair at night, a la 1900, so there will be fewer tangles in the morning, and it seemed to help.
It's more a problem for you than it is for your little girl, I think! :~) Your daughter just wants to try something different. In three months she might want to try something else different. It's the mamas who worry what will look good! I'd let her do her thing; she's only four, and if she says later, "Mommy, I don't like what my hair is doing," then you might say, "I always thought it looked better when...." That provides decision for her and input for you.