You can't optimise conversion if you remove the ability to track users. If you see 8 hits on page A and 4 on page B, is it that 4 people left or that the first 4 people visited the page twice before they moved to page B? You can't tell without the unique cookie.

That said, having a unique but anonymous cookie within a single site isn't the end of the world but Google only provide GA for free because it is useful for determining other things.