This may seem like a self-explanatory question, but if kinetic energy is a scalar quantity, and squaring the velocity essentially removes its vector quality, why not use speed instead?
I have a hunch that this might have something to do with how you derive it, but is it possible to derive the equation with just speed instead of velocity? Is it about keeping consistency with other equations? What is the reasoning behind it?
Because $\vec{v} \cdot \vec{v} = s^2$, where $s$ is the speed, this is a semantic question and has no practical impact. You can think of it as the speed squared, if you prefer.
This may seem like a self-explanatory question, but if kinetic energy is a scalar quantity, and squaring the velocity essentially removes its vector quality, why not use speed instead?
It is the same thing. For a velocity $\vec v$ the speed is $v=|\vec v|$. And $$v^2 = |\vec v| \ |\vec v|\ \cos(0)=\vec v\cdot \vec v= \vec v^2$$
