EVERYTHING HAS TRADEOFFS. Every single thing has tradeoffs. Obviously you should not write terrible, brittle code. The reason DRY is important is because when you start duplicating code, having 30 different serialization methods littered throughout your code, 5 different ways of calculating the same value, etc etc you see why it really matters. Its a GUIDELINE used to as a general rule. And as guidelines and general rules go -- its useful for juniors and people who don't have the experience to see the best way to write the code.
Its a good default, and like YAGNI, and 100 other programmer acronyms it has its ups and downs. Your pizza example is not "coincidental repetition" -- it is actual repetition -- you just abstracted it in a really poor way to make a strawman.