When you have a SWAT team as a hammer, even a 15 year old girl armed with a bow and arrow looks like a nail!
I'm not a big fan of the over-use of SWAT teams either, but I don't think this case is one of them. She'd just demonstrated her willingness to kill. Running off into her familiar woods she could easily take out a few individual cops before somebody got to her. With the team, there's probably a better chance of pinning her down, overwhelming her and taking her alive.
This is one of rare cases when use of SWAT is completely justified. First, she attempted murder already. Second, have you ever seen a broadhead arrow up close & personal? They are super-sharp, and they can take a grown deer in one hit. Arrows were one of main weapons of war for centuries for a good reason - they are deadly. Any common LEO who in search of this suspect walks into the forest without armor is likely to not walk out.
A 15 year old with a hunting bow who knows how to use it and showed a willingness to by shooting and trying to kill her own father.
That warrants a SWAT team, IMO.
If she’s willing to shoot her own father, she won’t stop at anyone else.