In classical music, the harmonic minor scale is used because harmonies based on a tonic/dominant scheme require the V7 chord to be major. Sharpening the 7th degree achieves this. It also gives a sharp leading note which classical music also prefers. The "unmelodic" augmented 2nd between the 6th and 7th degree of the scale is avoided by having yet a third minor mode scale known as the ascending melodic minor and this has both the 6th and 7th degrees of the scale sharpened. Before you ask, yes, there is a descending melodic minor scale which is the natural minor mentioned earlier. So, in classical music theory, there are three minor scales. Taking A minor as an example they are.

Harmonic minor: A B C D E F G# A
Melodic minor ascending: A B C D E F# G# A
Melodic minor descending: A B C D E F G A

In the past, most notably in Renaissance music it was common practice to end on a major chord even if the mode called for a minor chord, so that music in A minor would finish on A major. This was called a "Tierce de Picardie". This is because it was felt that a V-Imaj cadence was more complete than a V-Imin cadence. (or using classical music terminology, a V-I cadence rather than a V-i cadence)

Going back to the question in the OP I think the above indicates one reason for using the term "major" where it might be thought to be redundant and that is to avoid possible ambiguity. Another reason is possibly for emphasis - to make it absolutely clear you are referring to a major chord.

Going back to the accordion question, leavi