In major keys, plagal cadences often occur as IV-I - as it is supposed to be.
In minor keys, plagal cadences are originally supposed to be iv-i, but composers would often use a Picardy 3rd, making it iv-I.
So, the question is - why do composers often tend to apply the Picardy 3rd in plagal cadences in minor keys?
Popular in the 16th and 17th and going into the 18th centuries, a lot of minor pieces would end using a tierce de Picardie, finishing on the parallel major tonic chord.
Theory was taken much more seriously than it is today (!) and it was perceived that a harmonic from the root of the I chord that could be heard by some was the major third ( the fourth harmonic), so that would clash with the minor third of the final chord. Listen carefully to some voicings of final minor chords, and it's conceivable that this is true. That apart, after listening to something minor for a while, the major is a welcome mood changer!
This could spawn a corollary question - why is it called the Picardy third? The answer to which is evasive.
It's a choice. Either chord could end a piece (and there are some examples with the sampe phrase ending differently.) In some modes, the ending chord was always major; sometimes this practice would carry over to key-centered music.
I've found that some tunes I've written sound better with a minor chord ending and other actually sound better with the Picardy Third. I don't know why so I just try both and see which I like better.
On a similar note, (so to speak) in one of Bukholfzer's books, there is an arrangement of Greensleeves which uses minor v chords (and minor i) when a section has more following and a V chord on the final cadence (V-i). Sometimes it's just taste.
In playing strophic music (like hymns or songs) in a minor key, it's sometimes useful to play a V-i cadence at the end of each verse and a V-I to end the last verse; this signals the audience that something different has happened. (I might even use v-i internally, V-i at section ends, and V-I to end the complete piece. There's not much harmonic change but listeners should hear the section markers.)
