yeah this is especially noticable on closeups right?
you can turn up the poly count on those groups that cross the scalp
also you can change the thickness of the hair.  it always looks a little thin to me anyway at default settings.  but go to far with this and it gets a little anime.  (cool if you want it though)
you can try scaling a skull cap to fit the head maybe use magnets or something to get it very close, then load a texture to look like hair on the scalp. (some p5 default skullcaps have textures).  to get a good fit i would export head and skull cap to max and conform the skull cap, get it nice and perfectly close.
also when animating turn dampening up (possibly a lot) or the hair will just take off.
make sure the skull cap does not intersect the head at all anywhere and that no hair starts out in a "pose" that intersects any collision objects.
if you are gonna go with thin hair and close up renders, you are gonna have to increase the hair count drastically, and go for a walk or something during render
but its worth it for a great shot
good luck