I’m not so sure that log structure would reveal to you VeraCrypt style hidden volumes. It would only tell you about which blocks are allocated but the whole point is that VeraCrypt would allocate the whole space and within it have hidden space. You wouldn’t be able to infer (at least ethically, but you could lie) whether or not a hidden partition exists because you don’t know if the allocated block is present in the filesystem or was just allocated and never trimmed.
It would also give you information about the order in which blocks were written, and the historical state of the disk. Because of wear leveling, block allocation isn't just a one-time initial thing; the mappings between logical and physical address space are changing with each write.
> allocate the whole space
what do you imagine allocation is in this context? it's just a set of written blocks that mark address ranges and other metadata for the OS filesystem driver (all encrypted).
firmware metadata will leak the fact that there is churn in the address range where a potential hidden volume lies. the churn will be inconsistent with filesystem activity that would be present in its absence.
it's not just SSDs you need to worry about either, HDD firmware also keeps metadata, some of it could be be proxy to churn by region.