Like the phantom time hypothesis, bicameralism is a sort of massively revisionist theory that relies on wild interpretations of historical information. And both are pretty entertaining, regardless.
And the theories of Immanuel Velikovsky. Like the bicameral mind, the theories of Velikovsky are attractive to modern lay people because they give a "rational" explanation for mythology.
Nobody really knows how the modern human psychological consciousness developed. To compare a theory about that, to a theory claiming as-near-as-we-can-tell-physically-wrong things about Jupiter and Venus and Earth's rotation and physical forces, is invalid.
When I read criticisms of Jaynes, they seem a lot like criticisms of Darwin's original, simplistic view of evolution. Saying the bicameral mind is not a perfect theory is uninteresting; hardly anything is a perfect theory. What matters is the specific criticism (do you have one?) leveled at it, and whether the bulk of Jaynes's ideas can be modified and extended, with another few decades or century's worth of knowledge, into something that's roughly (empirically tested to be) accurate.
Nobody takes Darwin's original expression of evolutionary theory as gospel today, but it's part of the scientific canon for a reason. It was incomplete and therefore misleading in some ways, but the core ideas are essentially taken as true today. We can see evolution in action through microbiology and genome analysis, even if some specific (narrow) ideas and predictions by Darwin and early primitive evolutionary theory have been falsified.
Or look how relativity developed. First people were tinkering around with ideas about electromagnetism, discovering things about light, then came special relativity, which led to a bunch of problems, which led to general relativity. And even GR is wrong, since it doesn't currently accommodate quantum theory. That doesn't make special or general relativity wrong, so much as it makes them incomplete. They may be wrong in an absolute sense, but they're still quite useful. Even special relativity, being the wrong-er of the two, has some important "first step" realizations, like speed of light being invariant. Even the ether theory, now pretty much falsified, might end up having some contribution to future physics, if it turns out that there's some substrate (in a sense, though it would probably be neither matter-like nor light-like, and instead coupled to matter and light in interesting ways) that binds things together.