Also a weak battery will cause more wear on the starter as it can cause it to overheat due to the low amperage (current flow). This is forcing the starter to work harder.
I think I agree with that. If the battery has a low voltage, the amperage draw of a brushed starter motor will actually go up somewhat due to the slower rotational speed. Motors are usually rated in watts, and you'll get higher amp draw at a lower voltage. Electric motors and incandescent bulbs tend to poke holes in Ohms law.
I've had a few drinks on this fine Friday evening and may read this tomorrow and have a WTF was I thinking moment.