climbing in pitch mode can also lead to a stall.
Not unless you select a crazy angle of pitch. Set a normal climb NU angle, close the thrust levers and see what happens - Stall? No, just a descent. Turbulence or sharp temperature gradient - rides it nicely with very little fluctuation in speed (unlike v/s). In fact, pitch holds a remarkably constant Mach number all the way up the climb - I could complete a fiendish sudoku and not have to touch the AFGS!