No, ECC is not a mandatory feature in all SSDs- As you mentioned, NAND relies on ECC for proper operation, but then again, not all SSDs have NAND Technology. Some SSDs actually use the same technology that the RAM inside of your computer uses, but thats a different thing I won't go into.
Part of the reason that data protection is very important with SSDs is due to the fact that these drives somewhat have a set amount of times a user can erase data and re-write over where said erased data was- If you are constantly erasing data and writing to a data block where there used to be data, then your drive will essentially fail.
SSDs are still quite new technology, and with this, they still have unresolved flaws. One could say that what they have over the conventional HDD in durability and speed they lack in stability. Sure, these faults occur much less than they used to and don't happen nearly as often, but they are still there.
Unless I was using a low-capacity SSD as an operating system drive with my data on a separate HDD, I wouldn't trust my data with an SSD. Not yet.