I'd have to agree with the thought that there's no consensus.

I normally prime, caulk, then paint. Some say caulk first but,
obviously, I disagree - whenever I prep windows and I can pull out long
strips of caulking, it's normally bare wood underneath.

I think that whether you caulk after priming or after the finish coat
probably doesn't matter. The one factor would be how well you can run
caulk - if you can get a nice clean bead you could do it last, after
the finish coat. Otherwise, the finished product will look better if
you paint last.