Breaking this functionality breaks the lowest common denominator of data sharing: Taking a screenshot. One of the reason to make a screenshot is just because an application misses a proper data export functionality.
Also, QA and dev teams use Incognito for "clean" testing, and screenshots here are very valuable for showing others what you're seeing (especially if they're not in the same office or area), such as when they're pasted to a ticket board.
I honestly don't see the reason for this restriction; if it has something to do with Recents (which the source code change ticket implies), then I don't know how that makes sense either, as I have Chrome tabs in Recents disabled, and I can't see how this benefits the user unless Google employees' significant others busted their salacious Incognito usage... but that's punishing the innocent as well and telling every user they're not capable of "doing it right" even if that's their knowing intention.
If Google's Android really can't tell the difference between a physical user and a software app, there's something seriously wrong with Google or Android.