Well, as noted in my initial response, I believe a non-CRF rifle, such as the Remington, would be fine for a good many hunting situations and indeed in most instances, and possibly all of them. However, that isn't to say it's a 'better' action than a Mauser 98. You could for example probably do just fine on any DG hunt armed with almost any action type you liked, chambered in 30-06, but that doesn't mean the rifle, whatever it might be, is a good choice.

Unlike the Remington, the Mauser has a number of inbuilt safety features that make it about as reliable and safe as a bolt action possibly can be. CRF is but one of those features. And no, it's not essential to the operation of the rifle under normal circumstances. But neither is a safety belt essential equipment in a car - under normal driving conditions. But stressful situations, such as warfare and the hunting of DG for example, can make people do things that they normally wouldn't, like attempting to insert a round in a breech that already has a round in it. This is a common mistake. That possibility is largely eliminated in a 98 but not so in a Remington. If you mistakenly attempt to double charge your Remington while facing DG you may find yourself in the invidious position of having to immobilize the uncooperative brut with repeated blows from what is now, for all intents and purposes, a club.

And if you don't believe that sort of mistake would happen, just have a look at the records of muzzle loaders recovered after some of the battles in the Civil War. A surprising number of them were found to have been loaded, right to the muzzle, with un-fired charges.