Leadsled, relax.
The overspeed checklist I refer to in the Boeing 737NG QRH is a memory checklist. It specifically says to correct an overspeed by adjusting thrust, and if necessary attitude. It does not say to use speedbrake.
If I subsequently use speedbrake to arrest an overspeed when I could have just used thrust/attitude, and the resulting turbulent airflow causes damage the the elevator trim tab, I may have to explain why I acted contrary to the FCOM. (The early Boeing 737NG had issues with high speed speedbrake use on the elevator trim tab which needed an AD to address.)
The "out" which is referred to in a post above is available if the PIC believes that following the FCOM will result in a reduced safety outcome, or if the PIC believes that an alternative course of action will result in an increased safety outcome.
Sound knowledge of the FCOM and the experience of when to follow it or not is what determines who should be on the flight deck. It's not just WWII stick and rudder skills anymore. But yes, you do need to know how and when it is appropriate to hand fly the aircraft, and practice same when conditions are appropriate.