That makes it impossible to properly implement POSIX on top of it and seems like a poor design.
The correct design is to have both a "root" and a "current object" associated with every "file descriptor object" and allow ".." to work up to the "root" (and thoughtfully handle cases where the "current object" is moved outside the "root").
You can't do it with paths because that doesn't track directories being renamed, that would cause the descriptor to suddenly become inaccessible in the middle of an operation.
It depends on whether it's an attack against HVM hypervisors or not.
If it, like it seems, is just an attack on OS kernels and PV hypervisors, you can simply turn off the mitigation, since nowadays kernel security is mostly useless (and Linux is likely full of exploitable bugs anyway, so memory protection doesn't really do that much other that protecting against accidental crashes, which isn't changed by this).
Even if it's an attack against hypervisors any large deployment can simply use reserved machines and it won't have a significant cost.