I have also done a couple longish run streaks, but would have rested if ill.

Why do you run with the flu of you feel bad about it? What is the point of fulfilling the "rules" of run streaking?

For me the by far biggest positive effect of run streaking was that I knew every morning when I woke up that I would something i enjoy that day. The training is too low intensity and volume to really matter and doing it for the rules would have felt pointless.