There is no graphing problem that you'll be asked to solve before university that can't be plotted to a 'good enough for high school' level by hand in seconds.

Four data points is sufficient to give you a 'good enough' shape and position of a second-degree polynomial. Five or six for a third-degree one. (And you barely see them, and don't learn how to algebraically solve for their roots in high school anyways, because the cubic factoring formula is a pig.)

If you can't tell what a function's plotted shape is going to be at a glance, you haven't learned the material to the degree expected of an attentive child.

Life is not all about solving problems, high school life even less so.

Personally, I found great enjoyment in coming up with more and more involved plots in the Polar and Parametric modes, where yes I would predict what a graph would look like and then go over to see it. And then go back and iterate. Etc. Until I was painting pictures with functions and had a far greater understanding of the domain than I’d wager anyone who thinks graphing calculations are for finding roots of polynomials could imagine.

This is nonsense. Kids are not expected to look at polynomial equations and be able to deduce the shape of the graph without a graphing calculator. Besides, it is expected that a student can use a graphing calculator to be able to numerically solve for a root of arbitrary polynomial equation.