Cock on closing was the brilliant invention of some lost to time inventor.
It reduces the amount of effort on primary extraction to 1/2 that of cock on opening.
Perhaps most famous in the SMLE where the WW I Germans thought every Tommy had a machine gun.
As much as everyone loves the Mauser, the SMLE was a far superior battle rifle.
COO conversions are far too often a mess as well as unnecessary.
The most brilliant "modern" bolt action, Schultz & Larsen also split the effort because they knew a COO with a 45 degree bolt lift was a bad idea. Also like the SMLE they have rear locking lugs that shorten the bolt throw.
We know what action Roy picked for the first 378 BEEs, don't we ? Slicker than greased kitty litter !