But maybe Amazon is ready to rethink the Web.

Michael Calore notes a job opening at Lab126, Amazon’s consumer products unit that built the Kindle, for an engineer to help build “an innovative embedded web browser.”

It’s possible that Amazon (AMZN) is thinking about something other than the Kindle here. But a decent Web browser for the e-book reader is long overdue.

I understand why Amazon didn’t push the browser when it rolled out its first device in 2007–it had other priorities–but at this point, having a wireless device that only grudgingly accesses the Web makes no sense. And it certainly won’t fly once the Apple (AAPL) iPad ships next month.

That said, if Amazon does add a full-fledged browser to the Kindle, the ripple effects will be pretty significant.

I assume, for instance, that adding a real browser requires a conversation with AT&T (T), which is currently providing “free” wireless coverage for the device. The carrier’s coverage doesn’t tax its system very much right now, since Kindle users only really need to go online to download new books. But if they could actually use the Web, the equation changes.

And a real Web browser means publishers who are selling subscriptions to their titles via the Kindle will have to rethink that strategy, too.

I don’t get the point of paying $13.99 a month for a subscription to the New York Times (NYT) on a Kindle to begin with. But if you can get a decent version of the paper for free–and updated in real time–via the Web on the same machine, then there’s no point at all.

The Times is already working on a Web pay wall, of course. But adding a real browser to the Kindle may push other publishers to think even harder about walling off their stuff, too.