Electronic – Is conventional flow a real, physical thing or is it something we made up?

Now, this does get confusing when you get to semiconductor theory, and I understand your issue. I can name one very important case. When working with charge pumps in the human body. Many places in biology the charge flow is positive. When taking a biomedical modeling class for EE we often had positive charge flow.

We can get crazier, what if you have cancer? There are many options, sometimes you pick radiation. Photon radiation exists, what about proton radiation? The amount of protons they are sending are measured in Amperes. Why? Positively charged particles per second(enjoy the pun).

The important part here your particle makes an issue of. If electrons were positively charged the issue would be swept under the rug by most people. The fact that they are negatively charged makes people think about what it really means.

If you really get down to the physics it is just a sign convention and is a menial problem. If you would like to assign them positive charge please do so, be internally consistent and do not publish anything and no one will be the wiser.

The most important thing is that if electrons were positively charged we would not have nearly as great of a name for the positron. I personally would not live in a world were the negatron is a particle.

Electric current, A.K.A, "conventional current", is an abstract current, the flow of electric charge. From a previous answer I gave here:

Electric current is an abstract current, the flow of electric charge, not a physical current like, say, electron current, the flow of electrons.

But electric charge is a property of things, not a thing, i.e., electric charge is always "carried" by a thing.

So, while an electron current is necessarily an electric current (due the negative electric charge carried by the electron), an electric current is not necessarily an electron current.

For example, in a salt solution, we have two species of electrically charged ions present, the positively charged sodium ion and the negatively charged clorine ion. Imagine that the sodium ions are moving to the right and the chlorine ions are moving to the left.

Obviously, we have two ion currents in opposite directions but there is just one electric current and it must have a direction. The direction of electric current is, by convention, the direction of the flow of positive charge.

So, in this case, both ion currents contribute to an electric current to the right. The first term is due to the positive ions to the right. The second term is due to the negative ions to the left where the negative sign numerically "flips" the contribution to the electric current.

Think about it this way, if I told you that I was travelling at -60mph west, you'd know that I was actually going 60mph east. Similarly, a negative charge current leftward is an electric current rightward.