Well guys
Let me tell you how it's been for me.
I have been doing gunsmithing now for almost 40 years. I worked as the "roving gunsmith" in Western Nevada and the Tahoe basin on the Cal. side, as well as doing gunsmithing for several shops in Reno Nevada. I also used to do the same thing for several Wyoming shops and one in Montana.
So I have handled thousands and thousands of Remington 721s, 722s and 700s.
I have had LOTS of extractors to replace. Now most were probably never soaked in solvent, and so were not "cleaned", but I am not lying to you when I tell you that they do break sometimes. I also did "service center" work for a while, and I have replaced about 12 M-700 bolt handles that came off rifles in gunshops before they were ever sold. So xausa is right. It's statistically rare, but don't think it doesn't happen.
Now you may say "It could happen to any other rifle too" Well yes, it could. However, I can tell you from personal experience that I have had to replace lost (they don't break) extractors on about 3-4 post 64 Winchesters, and 2 Savages in 38 years, I have replaced one Weatherby extractor that was just not machined right, and I have NEVER had to replace a Mauser extractor except for the occasional one that someone messed up trying to open it up for a belted mag, and ground too much off. (not the fault of the part)
If we look at the statistics, you probably have maybe a 1-1000 chance of having your m-700 come apart, and if you will clean your bolt face, so brass shavings don't build up under the extractor, you have a very good chance of having your M-700 work forever. So I would never say that you are "going to have a failure" -- but I also would say (without any doubt in my mind,) that if you were going to have a problem with a bolt action, it's probably going to be a Rem-721, 722 or 700.
Now I don't do "modern gunsmithing" anymore for my living. I work only on muzzleloaders, and I have for many years now, so I can't say what repairs are common anymore. However I would point out something to you all;
Go to the Brownells catalog. You will see that in the back there are many pages of gun parts listed for sale. Pages and pages of them.
But in the front of the catalog you will find Rem-700 extractors have a special place. Not Winchesters. Not Savages. Not Sakos.(except for those to replace Remingtons) Not Brownings.
Not Weatherbys. Not Rugers. Not 03 Springfields. Not 1917 Enfields. Mausers? .....yes...(because of people messing them up in their attempts to modify them, in my openion)
But there's a special place for Rem-700 extractors. (page 95 in their newest catalog)
Brownells doesn't make them a high profile item just because they need to take up space on a page.

Ok.........
Now I am sure the flames will begin. It's OK. I will just go make a flintlock.

I have told you all what I know, and what my experience has been. Your belief-- one way or the other --- is up to you. You have my blessing either way.