So I've been getting into the math behind animations in video games, specifically Quaternions; and I've noticed that when extracting Euler Angles from a Quaternion, the Yaw is limited from $-90$ to $90$ while Pitch and Roll both get a full $-180$ to $180$. Since a Quaternion can describe every rotation in $3$ dimensions, would it be correct to say that 3d objects only need $2$ and $1/2$ angles to describe them?
As you have probably learned, by now, there are various different ways to represent the orientation of an object in 3D space. You can use a rotation matrix, a quaternion, Euler angles, or an axis and an angle, for example. But all of these have one thing is common -- they all involve three independent numbers.
So, I would say that your "two and a half" idea is incorrect.
Euler angles are limited to some specific range to ensure that they are uniquely defined.