That is in fact how crash dump works on illumos systems. Once you enter a kernel panic, interrupts are disabled, all other CPUs are brought to rest, etc. Then the panic code takes the pages to write to the dump and passes them to a special routine in the driver for the dump device: usually either a slice on a disk or a zvol). That driver is responsible for getting the device into a state where polled I/O can be performed, and to write the pages out. At the end the system reboots, and on the next boot a program called savecore inspects the dump device to see if there is a new dump, and if there is it transfers it into a new file.
FreeBSD does the same thing (probably some shared 80s BSD heritage?). One challenge is actually providing that special routine for the dump device in a way that is safe at crash time. You don't know how bad a state your crashed kernel is in, and some buses may not have a polled IO mode (USB?).
The Linux kexec process kind of elegantly restarts into a known state, with the known drawback of hogging some memory. It's definitely a different set of tradeoffs and both seem vaguely reasonable.
