Here's the problem: the woman receiving these threats has no way to know whether this is some teenager on the other side of the country or the creepy guy down the block. She has to spend time thinking about each one and wondering whether to be worried or not, or whether the harasser is going to escalate from being an ass on Twitter to contacting her friends, relatives, coworkers, etc. on email/Facebook/etc.
The one thing which I would bet on is that if something bad did happen – and given that her dad is a celebrity hated in some circles, that's less hypothetical than it might seem in your first reaction – there would be people coming out of the woodwork to ask why she didn't report it.
Unfortunately, the goal of prosecuting threats is to prevent violence, not prevent people from being scared. If the chance of violence is relatively nil, (I already argued that I believe these guys are just terrible, wanna-be comedians) I don't think there is any case to be made that these guys are anything near sexual predators, just assholes and scumbags.
The goal of prosecuting threats is because threats are violence, or at least are damaging in and of themselves.
Threats are also illegal under 18 U.S. Code § 875(c). Even if there was no intent to carry out the threat, if the threat can be interpreted by a reasonable person as being intended to cause fear, it counts as a true threat. [1]
The one thing which I would bet on is that if something bad did happen – and given that her dad is a celebrity hated in some circles, that's less hypothetical than it might seem in your first reaction – there would be people coming out of the woodwork to ask why she didn't report it.