Why is the sense of the electric field the one that goes from the highest to the lowest values of an electric potential? To clarify, what's the reason behind it and why is it not the opposite?
 A: We always consider the charge we do tests on to be positive. So think of a positive charge left in this potential, where would it want to go to?
Towards the negative plate, of course! So it experiences a force towards the negative plate, so the field is always directed to the negative plate hence answering your question: the field is from positive plate to negative plate i.e higher potential to lower potential, essentially due to a convention that all test charges are positive.
Also adding to this: Potential is simply the work done in moving an electric charge against the electrical field(force). That is why u have a negative sign, electric potential decreases in the direction of electric field as you would need to do work against the field.
You can also think of it gravitationally, Think about a physical hill. On the top of the hill the particle has the highest potential, as it rolls down its potential decreases. But the force due to gravity is pointing downwards so in the direction of the force the change in potential is negative.
We actually have a in-general relation for force and potential:
$F=-\frac{dU}{dx}$ which works for all kinds of forces, be it classical or electro-magnetical.
A: As I understand it, it is strictly a matter of historical convention that the direction of the electric field is the direction of the force that a positive charge would experience if placed in the field. A free positive charge placed in the field would then go from the highest (most positive) value of electric potential in the field to the lowest (most negative) value.
The convention could have been the opposite, that is, the direction of the electric field could have been the direction of the force that a negative charge would experience if placed in the field. In that case, a free negative charge would go from the lowest (most negative) value of electrical potential in the field to the highest (most positive) value of electrical potential.
Related is the convention for the direction of current flow. Conventional current is defined as the flow of positive charge, even though in the vast majority of instances current is the flow of electrons (negative charge). The convention was established well before the true nature of current flow was known.
Hope this helps.
