Do you have an example of this actually happening? I am aware of numerous examples of .308 Winchester cartridges being fired in .30-'06 chambers with no ill effects.

I don't get the significance of "if the rim jumps the extractor"? The ignition of the powder is going to slam the rimless case head right back against the standing breech or bolt face. At worst you might get a case head separation, if the case obturates too quickly and adheres too firmly to the chamber walls to allow this to happen.

And, as kuduae says, these are rimmed cartridges which don't headspace on the shoulder. No different than firing a .300 Winchester Magnum cartridge in a .300 Weatherby chamber.