No: your posture with respect to having to cycle servers is a super complicated subject and you address it both with process and with architecture (for instance: you can be blasé about things like CopyFail if you don't allow multitenant shared-kernel in your design in the first place). But no matter what process and design you have, if you're hosting sensitive workloads, you always have to be in a position where you can metabolize having to cycle your servers.
It's a category error to talk about a disclosure event like this as something that would destabilize someone's fleet operations. The Linux kernel is fallible. So is the x64 architecture. You already have to be ready to lock things down and reboot (or mitigate) at a moment's notice.
Remember: whatever else grumpy sysadmins have to say about this, Xint are the good guys. Contrast them with the bad guys, who have vulnerabilities just as bad as CopyFail, but aren't disclosing them at all --- you only find out about them when it's discovered they're actively be exploited. There's no patch at all. There isn't even a characterization of how they work, so that you could quickly see what to seccomp. That's the actual threat environment serious Linux shops operate in.
LPEs are not rare.