I assume you are talking Remington 700, correct ? There are other Remington actions. I have a .375 H&H Remington 30 Express, one of the best actions ever devised, essentially a M1917 in civilian dress. I also have another 375 on a Rem 798, which is simply a rebranded Zastava M98.
If you are talking the 700, or 721, or 725, the extractor is considered the weakest link. The .375, 458 WM, and 416 Remington all have the same case head size, other than pressure differences the function of the extractor should be the same. The .416 in the 700 did have a reputation of having issues with SAAMI max pressure of 65,000 as compared to the .375 H&H 62,000 psi. The 458 Winchester is rated for less pressure then the H&H, therefore I would expect less issues than either the .375 H&H or .416.
As Habib noted, installing a robust M16 style extractor is good insurance on a 721, 725, 700 in any of the belted mag cartridges if used for DG.