The reasoning I've heard why an IDE doesn't do that (as opposed to a beefed-up text editor) is that an IDE needs to continue parsing and analyzing even in the face of an error in your source code. Because, presumably, you still want features like "jump to the definition of FoobarClient" to work even if you've misspelled something in a header included indirectly by FoobarClient.h.

Compilers generally stop after the first set of errors in the first compilation unit. IDE indexers want to keep going as much as possible.