You can make use of merkle-trees when ever you want to proof the data integrity of large amounts of individually independent data (distributed FS etc).
After playing arround with SMTs for a bit, possible use-cases came to mind quite frequently.
The challenge to me is that the ability to prove the data integrity is quite hard once you store the data elsewhere, particularly on a single disk - I don’t know that people are regularly reading and reevalidating the stored data and likely not on every I/o operation.