Why are XP users stuck with IE8? It seems like such a weird tight-coupling. Almost all other applications seem to work perfectly fine with XP, Vista, 7 and 8. I don't really see why this specifically would need such a dependency.
Because that's a choice Microsoft has made.
Really. It's as simple as that. They have coupled the web browser very tightly to the operating system, and thus replacing it means replacing large chunks of the OS. Even if the differences themselves were to be relatively small, it'd still be differences and those need to be supported (coded, debugged, documented, tested, maintained, ...).
Note that this isn't even the same problem as removing the browser entirely; it's highly likely that for the type of integration done between Windows and MSIE, the APIs are quite different between versions of MSIE.
And of course, extended support for Windows XP non-Embedded ended in April 2014. So by now they have even less of a reason to support anything Windows XP.