Electrons

But then electrons(+) would have mass, would be in the nucleus, and protons(-) would have no mass.

Odd seeing something "pro" having no mass and is (-).

The convenience is not usually applied to defy atom models or to spread further confusion. It's usually used in the sense of electromagnetism and using charged sticks to induce charges upon other types of matter such as metal spheres and other conducting objects. In such systems it's usually presented that an object of matter has either a completely positive or a completely negative charge. It would be extremely inconvenient to fool around with signs when it's a system that has mixed charges in order to sustain it's constitution such as the Niehls Bohr model of the atom.

If you were to switch up the signs, you wouldn't change the attributes of the elements being discussed. For example, only electrons can be transferred from one object to another. Just because we decide to associate protons with a (-) charge for a certain problem, we are not giving it the ability to hop to different objects. If a problem requires analysis of an object and it's electrons being transferred back and forth, usually it follows common sense not to fool around with signs. In such circumstances it is absolutely unnecessary and only causes more problems.

As I stated before, context is essential not only to Physics but the sciences as a whole. If you were only dealing with all negative electron charge, then you wouldn't need to really bother with the inconvenience of putting a negative sign on every single charge because in the problem, there is only negative charge. That isn't going to change. You just have to remember that for the final solution you have to include the negative sign. And for grading purposes, to just put a negative sign at the end to all the negative electrical charges as an after-thought. Keeping the electrical charge negative isn't necessarily essential to the problem as you are only dealing with a system that is solely composed of negatively charged electrical matter. There's thousands of cases where signs do matter. It's just that there are also cases where you can make life easier for yourself. So why not?