The 10° pitch up will not make you climb, you need 12°. Try it in the simulator, even after pos-rate/gear up. Set 10° and you climb.
I don’t have access to a 737 sim any more but I suspect that if you left it at 10deg for a bit it would as the airspeed increased. My understanding is that the recall pitch/power settings are designed to put you somewhere in the middle of the speed range, well away from stalling. At high altitudes you’ll get a descent and low altitudes a climb, once you’re in a steady state. Maybe that’s why they changed the drill comparatively recently to use AA, in that it leaves room for this to happen? I’m on the 777 and this technique only made it into the FCTM in the last year or two.
