Hmmm, this is not what I would have expected, frankly. One of the main
advantages of Fibers are their low creation/context switching/termination
overhead. I would have expected for Fibers to be freely movable between
kernel-threads (work-stealing!), even more so as you expose an interface
conforming std::thread... If Fibers look like threads, they should behave
accordingly.

I think that it is too over-constraining to inhibit moving Fibers between
kernel-threads just to maintain NUMA awareness (not all architectures have
those in the first place). The decision whether to move a Fiber or not
should be entirely left to a scheduler/executor (which could confine a Fiber
to a NUMA domain, for instance, if needed).

Also, it should be made very clear that the use of Fibers has certain
implications on using TLS (in short - don't use TLS, but FLS instead)

Thus the fact whether compilers cache the TLS or not is mostly irrelevant.