I tip that will likely save all Remington shooters grief in their futures is simply to put a drop of Hoppes #9 on the bolt face 1-2 times a year. Just enough to wet the area behind the extractor. It need not be dripping, just lightly wet.

If you look at how the extractors are placed in the bolts you'll see that brass powder from the scraping action of the extractor tooth is likely to build up BEHIND the extractor. When the race gets full the ends of the extractor are forced to do all the flexing, instead of the entire circumference of the clip doing the same thing. In other words, 20% of the clip is doing 100% of the work. That can cause a stress crack.

I drop of Hoppes will dissolve the copper in the brass powder and turn it into liquid. And Hoppes doesn't ever attack steel.

Just doing that alone would probably eliminate 99% of the cases of broken extractors I have to replace.
I would rather a shooter clean his Remington Bolt Face then clean his bore. A fouled bore will not shoot as accurately, but it doesn't cause the gun to break.