My first centerfire rifle was a 1917 Enfield, so I find the cock on closing to be at least as "natural" as the cock on opening rifles. The effort seems less to me on the cock on closing versions, actually, but each person has their own likes and dislikes.

The only thing I don't like about cock on closing is the extra effort can disguise a problem with a particular round and how it chambered. Rare condition, I know but after 35 years of handloading I like to "feel" each round close home.