My wife and I are both musicians. Playing a Picardy third is a quick way for me to get asked to sleep on the couch (only exaggerating slightly).
I love using a Picardy third when accompanying sung music and the text demands/suggests it. An open fifth is also a good tool for emphasizing certain texts. Just like other strong effects (deceptive cadences, modulations...) it's best effective when used sparingly.
In my youth I was "volunteered" to play piano accompaniment at church. There was probably more respectful way to get out of it, but closing minor-key hymns w/ a Picardy third, and major-key hymns w/ major or minor seventh (depending on mood), got me removed.
Next time you're feeling mischievous, try an "anti-Picardy third": end a major key piece (e.g. Pachelbel's Canon, US National Anthem, Silent Night, Happy Birthday...) with a minor chord.
When I was a kid I enjoyed annoying my parents by transposing random major-key songs into minor. I used to love doing this to "Joy to the World," among others, only to find later that the H.P. Lovecraft Historical Society had the same idea: https://www.youtube.com/watch?v=ptP0OR-e7rI.
There's a genre just starting where people electronically modify old recordings to change key. John Denver's Country Roads actually makes more sense in a minor key, to me at least:
Scientifically proven: Once every three gigs, and no more than once per every five performances of any given song across gigs. (For small jazz combos; St James infirmary is a pretty common one to get the treatment).
I love using a Picardy third when accompanying sung music and the text demands/suggests it. An open fifth is also a good tool for emphasizing certain texts. Just like other strong effects (deceptive cadences, modulations...) it's best effective when used sparingly.