Hammerless guns are cocked on opening (the vast majority of them). So you are carrying around a COCKED gun when using a hammerless or repeater.
The safety blocks the trigger NOT THE HAMMER. So a gun on "safe" is not safe in an accidental hammer fall. The hammer can fall with the safety on.
Consequently this preoccupation with cocking the hammer gun is a little misplaced unless you do the same with a hammerless, ie, carry it open and close it on mounting the gun.
It is perfectly safe to cock the hammers when in an active hunting phase, ie behind a dog on point or at the stand when pass shooting. All other situations call for an open gun, regardless of hammer location.
The notion that walking few steps with a cocked hammer gun is somehow more dangerous than with a cocked hammerless on "safe" is weird. At least a rebounding hammer gun has a safety notch to catch the hammer in an accidental hammer fall, while your Anson Deeley SXS, OU, pump and auto do NOT.
Dismantling a few guns and seeing how they work is an eye opening experience.