Someone recently said "derived/triangulated categories are an abomination that should struck from the earth and replaced with dg/A-infinity versions". I have a rough idea why this is true ("don't throw away those higher homotopies -- you might need them some time in the future"), but I would be interested to have a more informed/detailed understanding of why triangulated categories are so abominable.

So, my question: Where are some good places to read about this "Down with triangulated!" philosophy?

I'm interested in this because in my research I have come across some categories which, very surprisingly, have a (semi-)triangulated structure. Perhaps I should be looking for an underlying A-infinity structure.