As usual, I love Fran's advice.
Suggesting something like a haircut is in no way asking someone to change themselves or pretend to be something they're not. It's a hair style. I have had my hair long and short, straight and curly... yep, I might prefer a certain style (but my preferences cchange daily), and certain styles might attract more notice than others, as well. But it doesn't change ME. It's not an act I have to keep up.... it's just hair.
And yeah, I definitely notice people more if I think they have a rockin hairstyle or a sweet pair of shoes, or what have you. It's not that good hair is a prerequisite for me wanting to get to know you, lol but it's what draws a person in initially.... if you are trying to MEET people, it's your appearance and the way you carry yourself that is going to make someone want to get to know you instead of all the other people that might be around.
Not that a hairstyle is necessarily going to be the thing that makes men chase her, but it doesn't hurt to switch it up.
So no I don't think there's anything wrong with the suggestion being made. It mostly depends on how you say it. Would I bring it up out of the blue, nope. But if she vents to you about it, and you casually suggest that maybe trying to spice things up with a new haircut would help... I think you'd be fine.