To answer your question: "Is it safe to reuse a crashed SDcard?"
- If the crashed card boots, and has not gone read-only, generally
safe. - If the crashed card won't boot, but reformats to empty, generally safe.
- If the crashed card boots, but has gone read-only, it is generally worthless.
- If the crashed card won't boot, and won't reformat to empty, totally worthless.
(SDcards have a read-only safety feature to attempt to preserve data when the card detects damage has occured.)
BTW, the OS is probably caching your "continuous writes to /var/log", but any critical application or critical data deserves an UPS.