The logic behind waiting for the boat to stop relative to the jetty is there is a lot less chance of getting caught between the jetty and the moving boat.
Crush injuries between jetties and boats are too common.
The advise also stops novices thinking it is alright to jump between the boat and jetty. Crew often don't appreciate the movements of a boat and one of the scary things as a skipper is closing on a jetty, positioning the hull so a line can easily be slipped over a bollard when a crew member jumps believing their being on the jetty is going to make the securing of the drifting boat easier.
My docking technique does not plan to have anyone leave the safety of the boat until a line is secured and the boat secured and stable near the jetty.
Larger boats might be more stable but the risk is still there. Best seamanship is to develop docking techniques that do not rely on people on the jetty or moving from the boat to the jetty until the boat is secure.
Most times I back in to the jetty at 45 degrees tying a line from the rear to the jetty then motor forward against the line to push the bow into the jetty. Alternatively I run a line from the cockpit to midships then lead to the stern(outside), back the boat in at 45 degrees, secure the line on a bollard then use the line to haul the boat in sideways.
Both methods allow me to watch the clearances from the helm and I can power forward clear of the jetty if anything goes wrong. Its a simple procedure that works single handed and works from the safety of the cockpit.