I think you're right that women fear being perceived as "low value" if they ask a man out. I would add they also fear coming across as "easy," or even "desperate." And sure, some men might have the "since she's throwing herself at me, I migth as well take it" mentality, but not all.
The reality is that a good man won't have these kinds of thoughts about a woman who's asking him out, and if he does, he's not worth her time. Some men also pursue women with the intent of hooking up and leaving it at that, so refraining from asking a man out for fear he might be a player won't keep other players from chasing you.
The truth is that attraction and dating are risky, for both men and women. I have asked men out, and I have done my best to show men I like that I do like them, and would be open to them asking me out.
It does feel good to be "chosen," but it also feels good to find out your interest is reciprocated.