In InnoDB, crc page checksums are written as dirty pages are flushed from the buffer pool. On read, these checksums are verified. If the checksum fails, the server crashes awaiting intervention (startup with --innodb-force-recovery=N). At least for InnoDB, the cost is very little, since it takes microseconds around an operation that takes about milliseconds. The storage cost is also minimal.
This is very helpful in failure scenarios. Check/repair in mongodb can currently only detect meta data corruption!