Where abouts in the B737 FCTM does it mention 3secs/100AAL ?
I know we do it but I have never seen it!
My current FCTM mentions adjusting heading and timing so ground track does not exceed obstruction clearance distance.
I recall a note in the FCTM mentioning along the lines that timing is no longer needed due to GPS and the use of the FMC (fix page). But this might be for a visual approach.