Well, first I'll point out that many arrowheads were made of bone.

But generally speaking, if you're hunting or trying to kill a person, you want a fairly broad head on your arrow to cut into and cause a lot of bleeding in the target. When working at archaeological digs in North America, I encountered stone arrowheads on a weekly basis, and stone flakes left over from knapping appeared in almost every load of dirt taken out of some grid squares. Stone arrowheads are simply astonishingly common finds for archaeologists.

We also know from a few finds, like Otzi in the Alps, that rifling was known to prehistoric people, and they fletched their arrows to spin for a stable flight. Ancient and prehistoric people were just as clever as we are today, and when they put the effort into making arrows, they made them as good as they were able, and that meant arrowheads.

It's it possible that sometimes a hunter might make an arrow, but was unable to locate any good stone, so he just sharpened a wooden point and hoped he could kill something with it? Sure, it's perfectly possible. But after his kill, he probably would have sharpened the animal's bone into arrowheads for next time.