I saw some stats from Florida a few years ago and you were about 3 times more likely to have a LEO go bad than have a permit holder commit a crime. I think the percentage came out to be like 0.017% or something like that.
Even revocations of permits is usually tied to non firearms offenses. I think FL had like 8 or 9 permits that they revoked because of weapons charges in a decade or so.
*I like to quote FL stats because they basically invented the modern Shall Issue permit, they've been doing it the longest so you can look at the long term trends and numbers AND they make their stats available.