As AmiMoJo also noted, when you have a kernel panic all bets are off regarding which parts of the kernel are OK. If the behaviour of the disk driver or filesystem have been affected, it could damage your filesystem to try to write a kernel dump into a normal disk partition. It might work but it does seem a good idea to be properly paranoid. I didn't know that Windows uses a special reserved area of the boot drive - that does make sense as a solution!
There have been various systems for crash dumping under Linux, though. I think the de-facto solution (the one that was accepted by the kernel devs) ended up being kdump, which is based on kexec (kexec is "boot directly to a new kernel from an old kernel, without a reboot"). This allows full crash dumps with (hopefully) decent safety, so it is possible to do this if configured.
In kdump, you have a "spare" kernel loaded in some reserved memory and waiting to execute. When the primary kernel panics it will (if possible) begin executing the dump kernel, which is (hopefully) able to reinitialise the hardware and filesystem drivers, then write out the rest of memory to disk. I'm not sure how protected kdump's kernel is from whatever trashed the "main" kernel but there are things that would help - for instance, if they map its memory read only (or even keep it unmapped) so that somebody's buffer overflow can't just scribble on it during the crash.
Obviously, having a full kernel available to do the crashdump makes it easier to do other clever tricks, in principle - such as writing the dump out to a server on the network. That's not new, in that there used to be a kernel patch allowing a panicked kernel directly to write out a dump to network, it just seems easier to do it the kdump way, with a whole fresh kernel. Having a fully-working kernel, rather than one which is trying to restrict its behaviour, means you can rely on more kernel services - and probably just write your dumper code as a userspace program! Having just installed system-config-kdump on Fedora 20, I see that there's an option to dump to NFS, or to an SSH-able server - the latter would never be sanely doable from within the kernel but pretty easy from userspace.
Various distros do support kdump. I think it's often not enabled by default and does require a (comparatively small) amount of reserved RAM. So that's some motivation for basic QR code tracebacks. I suppose another reason is if they expect they can mostly decipher what happened from a traceback, without the dump being necessary - plus, with a bug report you can easily C&P a traceback.
This discussion has just inspired me to install the tools, so maybe I'll find out what it's like...