Return of the Data
At the current state-of-the-art, the idea of yet another storage tier using TLC is worth discussion, but it isn't a feasible play yet. Any backup device has to guarantee long-term retention of the data, and a low error rate on that data when it is restored. This is especially true of highly de-duplicated data.
Looking at restore, there are a couple of modes involved. Restoring a single file is a random access event. While flash will be faster, the overhead of loading programs, selecting files etc will swamp the speed difference. In batch restores, the issue is sequential throughput, where flash has a much smaller edge over HDD. Here, the cost per GB of HDD is so low compared with flash that extra drives are affordable, and the backup array can thus be lifted up to flash levels and still be cheaper.
Flash backup isn't a near-term proposition, except perhaps in Mil-spec applications. Ultra-rugged HDD modules for distributing movies to theaters could be replaced by flash, but the capacities involved probably don't require TLC.