But it could. It is apparently possible, with sufficient effort and ingenuity, to install OSX on the eee, although doing so violates Apple's licensing terms, which only permit installation on Apple hardware. So far as I can tell, the result is not only illegal but pretty flaky—people who have done it have difficulty getting various parts of the software to work, and doing it seems to require multiple tries and not always succeed.
Suppose that Apple itself took over the project. They, surely, could produce a version of OSX that would run smoothly on the eee. Further suppose they partner with eee to produce a slightly more expensive model, perhaps with a faster processor and more RAM, intended to run apple software. I, at least, would buy it.
One obvious question is to what extent such a machine would steal customers from Apple's more expensive models. The eee is not much of a substitute for a desktop, but someone who already had a desktop and needed a portable might buy a $700 Mac eee instead of a more expensive Macbook. On the other hand, the eee is both cheaper and smaller than anything that Mac offers, so would appeal to a lot of people who would not otherwise buy a Macbook.
I don't expect it to happen. But one can always dream.
A little more research turned up an ingenious, if implausible, solution to the licensing problem. The Apple license refers to "Apple-labelled" hardware. So you take an apple logo off an old Mac, glue it onto your eee, ... .
I have a feeling it isn't going to fly in court, but it definitely deserves a gold star for effort. For additional details, see the link.