Note that adding cooks *increases* cooking time...

Hehe! And also:

• "The bearing of a child takes nine months, no matter how many women are assigned."
• "Adding manpower to a late software project makes it later."

(Both from Frederick P. Brooks's "The Mythical Man-Month".)

But... is the person you're answering to really talking about adding cooks or about adding ingredients? Well, I guess it may well be a matter of personal taste and interpretation, or pov. And anyway... does adding ingredients increase cooking time? In principle yes - obviously. It all depends on whether it does so negligibly or considerably, and how good the final taste will be!