[Sabertooth]

When someone picks up a rock in his hand and strikes it repeatedly against an anvil of some kind (another rock, typically), it acquires an identifiable pattern of pits and scratches that remain indefinitely.

The key word being "repeatedly," meaning the same favored rock gets used. That means some practical place to keep it.

But stone tools can be much cruder than that, if the rocks are used once and then discarded. And no consistent wear pattern would result.

[Physicist]

The key word being "repeatedly," meaning the same favored rock gets used.

I could be wrong, but I believe the threshold for "repeatedly" is only a few whacks in one spot, enough to distinguish it from the natural bumping and grinding of stones. A couple of nuts should do it.

[Physicist]

Oops, I forgot the second part:

But stone tools can be much cruder than that, if the rocks are used once and then discarded. And no consistent wear pattern would result.

That's true, but then, there's no need to carry those. If tools are the key to bipedalism, "favored" rocks (as opposed to single-use rocks) would appear around the same time as bipedalism.