If an object is sitting on a potential slop, why must there be a force to push it into the well?
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Exactly, it is the force. If there is a conservative force, a potential can be defined as a function $U(\vec{r})$ that satisfies $$\vec{F}(\vec{r}) = -\nabla U(\vec{r})$$ Therefore the force pushes towards the minimum of the potential.
The common image of a potential "well" into which the objects "fall" is a great analogy because if you consider the gravitational force field here on Earth, $\vec{F} = -mg\hat{z}$ and so $U = mgz$. In this case a "physical well" (like a hole in the ground) is also a "potential well", because $U$ is proportional to $z$.
But one should be careful not to bring this analogy too far. In general a potential is just a way to express the fact that there is a force, and has nothing to do with height and falling.
Prallax
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It is because of the principle of minimum energy, which states that for a closed system the internal energy will decrease and approach a minimum value at equilibrium.
