The 1886, Win 1895, both have controlled round feed to some extent. The 1895 being an actual military rifle in the trenches.
The whole argument against CRF is kinda obsolete at this point, can anyone explain what is the advantage to push feed? The world has moved on in manufacturing. Basically the model 700 came up with a clever design where the action was not inherently more accurate than some other designs, but it was vastly easier to index into a conventional lathe so that you could blueprint it. This was a key to superior accuracy. It is basically irrelevant in the modern world where CNC manufacturing can make any action to the same tolerances. They don't have to look like a tube. There will still be stiffer types and types more ideally suited to accuracy. Today you can get super grade accuracy actions in series where controlled round feed is just one of the options. Or if one is on a budget, good M98 actions are still relatively thick on the ground.
In addition, there are a number of new CRF actions being designed all the time, that use different principles for CRF that are potentially more conducive to high levels of accuracy and reliability. I don't at this point see an advantage to having a manually operated action without the reliability features that are battle proven if there is no downside to having those features. And currently there isn't.
In the case of lever action stopping rifles hyper accuracy is not an objective anyway. It isn't as though I need to choose a lever action type just so I can send it off to a local gunsmith to be worked on and blueprinted. Some of the modern lever guns deliver bolt action accuracy out of the box, but that is not the main reason for owning them. If 3 MOA was a classic prescription in the past, a lot of levers offer 1MOA for 3 round groups. Even if you shot 5 rounds, they are not going to open up to anything like 3 inches. More than good enough. I just bought a Chiappa and the action is CNC milled, even at that price point. Probably the case for the Winchesters also. We are producing lever guns to standards that the original Model 700s only used to meet after a visit to the smith.