What's the point of having the ground near the negative terminal when
the electrons would just then flow out of the circuit into the ground?
No, if you measured the current with a meter on ground, you would find that there is no current flowing from this circuit to earth. Why? because all currents must flow back to the battery. A current needs a loop and current flows back to the source.
Since there is already a potential difference between the positive and
negative terminals, what's the point of a ground at all?
In this case, for reference. If this circuit was detached from ground, you wouldn't know what the voltages were with respect to ground. It enables you to call 0V the same as earth ground. This can be nice if you have other devices that are connected to ground. If this circuit is in the air, the whole circuit could be floating to different voltages (but they would be the same with respect to each other. In calculations, you need a ground, if there is a system of equations, you need a zero point or it becomes difficult to solve the system of equations.
Why would ground be on the right?
It doesn't need to be, you could put it anywhere in the circuit, the voltages would be different (relative one to another) but the currents and powers would all be the same.
It would be a great exercise for you to solve this circuit by putting the ground at different points and solving for all voltages and currents.