Let me try to approach this from a slightly different angle:
What would work as a citation form?
A good citation form would be such that you could deduce all other forms (from the perfect stem) from it.
I will look into the six personal forms of present active indicative and the present active infinitive.
The exercise can be extended, but these are a natural ...
For practical reasons, I imagine the index form is often (but not always) given in the first-person since it comes first in the principal parts and is usually the first in a paradigm memorized.
There is however ancient precedence. In discussing Latin verbs, Varro chiefly (but again not always) gives the first person unless he was specifically discussing ...