The square headed kind?

Fluted points are overrated. Madison triangular points are waaaaaay cooler

Oh look, another storage pit full of pot sherds and random faunal remains. Maybe a rodent burrow or twenty

Eh maybe. There is a reason they were replaced in the manner that they were in many cultures. For example, along the Great Lakes we see that many cultures begin to replace stone points and knives with copper elements scrapped from copper trade goods as soon as they had access to the trade goods. Copper was easier to work with, easier to rework, and simply just sturdier than a stone tool. Once the British and French started trading copper pots we suddenly see that everyone is obtaining these pots and dismantling them to use the copper for tools. Parts of the rim would become knives or fishing hooks, for example. I'm generalizing for a bit, but the biggest reason people went away from stone tools is that they can be finicky to work with. I flintknap in my free time, and it can be VERY frustrating to spend an hour on a point only to have it break because I hit in incorrectly when trying to break a flake off.

May I interest you in way too much info about projectile points?

That's a the awesome part about archaeology. There is always someone who knows way too much about a material or item used in the past. It's also why my wife never asks me about stone tools but thats whatever haha