Why didn't they simply let grow his natural hair?

For several reasons, I guess. First, time constraints - the concept designers began to work on the concept art in 2002 and the filming was scheduled for 2003. But most importanly, Anakin’s hairstyle wasn’t supposed to look the way it does in ROTS. Originally, George Lucas chose a concept with much longer hair which was bound into a ponytail. He wanted to make it similar to Qui-Gon’s from TPM to emphasize Anakin’s independence, his rebellion against the Council and also, to make him look dashing.

So you see, there was no chance Hayden could have grown 20 cm of hair in less than 12 months. However, when they tried the hairstyle prior to principal photography, both Hayden and George felt that the long hair made Anakin look too pretty, so in order to make him look more rugged they decided to shorten it until Hayden felt comfortable.

Considering that basically no one noticed and pretty much everyone thought it WAS HIS REAL hair (judging from all the suprised messages and reactions I’ve received), they have done an amazing job.