QM is the only bit of physics where something can still be both physical and have zero information content. Therefore it's the only place where the difference matters between C being a universal Vs a limit for information.

Also waves are non local, an exponential decay never actually reaches zero. Accepting this is critical to QM making sense. It's just very alien to our natural sensibilities.

As for the conflict with GR, both theories are known to be incomplete since neither predict each other. Knowing how both differ is one of the few known holes in physics. Interestingly, both theories are ridiculously accurate, within their domains, making the job all the harder.