I'm not making myself clear. It's clear from what you say that if Heraclites bought an ox yesterday, he owns an ox today. But in order to say that he owns this particular ox, he needs a better system of identity than "you never step into the same river twice".
It's a sensible system for deciding how to buy and sell oxen because it minimizes shipping costs. It's a less sensible way to, for example, judge the value of a person. Should I choose Alice of Bob just because Bob is at the beginning of a world-line and Alice is not?
This does kind of come back to arguing definitions. The common idea of identity is really useful. If a philosopher thinks otherwise, he's overthinking it. "Identity" refers to something. I just don't think it's anything beyond that. You in principle could base your ethics on it, but ...
Here's the new thread for posting quotes, with the usual rules: