As someone who was forced to learn Palmer style in school, I must say I always hated the capital Q. I don't know if I just couldn't get it right, or I never really saw it as legible, but it annoyed me that it looked too much like a 2. I went back to block letters in college and never thought much of penmanship.
Until college, when I learned a bit of LaTeX and became fascinated with fonts. Still hate that Q though. Thank goodness for computers.
That said, "the writing of the business world" today is Times New Roman (or maybe Helvetica Neue). It replaced the Palmer Method of Business Writing[1], which is quite distinct from the the cursive that is taught in schools today (Zaner-Bloser[2] or D'Nealian[3]).
1: https://en.wikipedia.org/wiki/Palmer_Method
2: http://content.yudu.com/web/y5b2/0A3vbrb/16Grade6Student/htm...
3: https://en.wikipedia.org/wiki/D'Nealian