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Taylor series approximates functions using infinite polynomials, so technically you're not wrong when you say "functions are polynomials." You're just... aggressively oversimplifying to the point where your calculus professor would need a stiff drink.
After grinding through Taylor's theorem for two hours, your brain apparently decided that all functions can be represented as polynomials and called it a night. Sure, analytic functions can be locally approximated by their Taylor series, but that doesn't make trigonometric, exponential, or logarithmic functions actual polynomials. That's like saying "all food is pizza" because you can technically put anything on dough.
The bell curve accurately captures the journey: most people understand there are many types of functions (normal distribution), while the sleep-deprived math student and the enlightened mathematician both arrive at "functions are polynomials"—one through exhaustion-induced delusion, the other through the profound realization that polynomial approximations are everywhere in analysis.
