Why does heating finished cold brew not turn it into a normal hot brew?

Answer: The cold extraction already selected which flavor compounds stay in the cup.

The cold extraction already selected which flavor compounds stay in the cup. ✓ — Right. Heating a finished cold brew changes only the temperature it is served at, not the way it was made. The cold soak let water draw flavor from the grounds slowly, so the acids, oils, and dissolved solids in the cup were chosen hours earlier. Warming the drink shifts how aroma reaches your nose, but it cannot dissolve anything new out of grounds that are already gone.

The added heat destroys the caffeine that the cold extraction dissolved. — Not quite. Ordinary reheating does not boil caffeine out of coffee; the caffeine stays in the drink and shows up when both hot and cold brews are measured. This option gets one thing right, that heat does change a cup, but what it changes is temperature, not the loss of stimulant. Hot brew and warmed cold brew differ because the flavor chemistry was fixed during brewing, not because caffeine disappeared.

The added heat rebalances the water minerals into a fresh hot-brew profile. — Not quite. Minerals in brewing water do shape how extraction runs, so it is reasonable to think they matter here. But that influence happens while the water is still touching the grounds; once the drink is filtered, reheating cannot rebalance those minerals into a fresh hot-brew profile. The cup carries the chemistry its original extraction produced, and warming only adds heat.