Nice question.
First of all, the IS a gravitational potential. I use to call it $V_g$ or $V_{\vec{g}}$, while the electric potential is $V_E$. "Potential" itself is as used as "potential energy", at least in my surrounds.
Secondly, there is a high issue with this notation. Many books decide to write $\phi$ for the potential (Greek letters for scalars, but that's absurd because $W$...$U$... are also scalars). Then, many books call kinetic energy $T$, and potential energy $V$. This is very upsetting to me, because it has just conquered everything, and the logical notations $E_k$ and $E_p$ have been just deposed. For me $T$ will always be period, and $V$ always volume (but I've got used to the other one, I can work with it without problems).
What I'm trying to say in this apparently off-topic paragraph is that all this has lead many people to say $H=T+V$, and at the same time"The particle is under a potential $V$". In other words, many people say potential when they mean "potential energy", for lazyness and also because of this notation. They know what they are doing, but they say it wrong. They're sometimes mixing concepts in speech (altough they understand it correctly). Students use to suffer this so much.
And finally, the potential itself is more used because it doesn't directly depend on your system. I mean, you can have an empty space with a certain potential. When you place the charge, the charge will get the corresponding potential energy. Now, there are so many systems in which you can somehow keep the potential constant.
For example, a battery supplies a constant potential to a conductor. In fact, in lab you do not have any source of potential energy, but a voltage source. If the system is such that charges do not affect the source of potential (or not significantly), then you have the same potential, but you can add many charges, the total potential energy is different and the potential can be constant.