With enough time and resources, any mauser action in good condition (M98 variant) can be made to work quite well BUT by design, it lacks features precision shooters prefer.
Does it mean it can't get to the 2's and 3's? No, been there done that a bunch of times. Can it get into the 0's and 1's? far more problematic and likely futile. And if you did, likely, there isn't much Mauser left.
Like trying to build a high RPM pushrod motor - there are simply better ways to get better results.
The round tube Rem has been the darling of precision shooting post WWII mostly because it was very easy to set up to machine.
Square bottom receivers need more fussing. Today, square bottom receivered actions are all the rage and actions like the Surgeon and PGW are selling extremely well. Round or square or octagonal really doesn't matter. What does is the properites at lock up and ignition. Here there are many ways to skin this cat and many approaches are being taken today with superb results.
It has far more to do with how the part is made then the design of said part.
As for Savage action clones, there are more then you may think and the concept is now pretty much being used (whole or in part) by most every rifle maker in the US. There are even custom actions merging the benefits for both the Savage and Rem doctrine.
Whether a prefit/barrel nut headspace barrel will work well on a Rem receiver, depends on how wonky the receiver is in the first place. If there is poor lug contact with the receiver, out of alignment threads vs bolt face vs lugs, floppy undersized bolt, the most I would expect is varmint grade performance. This has everything to do with the variations at lock up and ignition (slop allows the bits to move around inconsistently). The barrel itself can perform just fine (assume all machining and barrel quality are sound of course).
So when shooters talk about how Rems are used, etc, etc, they most certainly are not talking about a box stock receiver and a barrel swap. Alot of skilled TLC has been applied at a cost. Why we have custom actions in the first place...
As for the generic Savage/Stevens/Axis, that is a completely different story.
Jerry