I wonder how much of the lack of QA is rational. That is to say, for most projects does shipping with lots of somewhat hard-to-find bugs actually hurt the bottom line?

For some classes of bugs it can (e.g. if the software is so bad as to open you to a class-action lawsuit; in b2b software bugs that put you in breech of contract), but for many classes of consumer software, it's not clear to me that shipping software that works better is rewarded. Picking not-too-buggy software ahead of time is hard, people are slow to switch (even when the people encountering the bugs are the people selecting the software, which is often not the case), and people are good at subconsciously avoiding triggering bugs.