A use case for this is a marketplace where products are public but purchases of those products remain private.
But I guess we can't go around certain difficulties:
Bridge-level privacy can be improved by batching, delayed settlement, relaying, avoiding unique amounts and increasing the number of users sharing the same shielded pool.
This requires many users for aggregation to be viable. And even then there can be many situations in which someone is able to correlate data and sufficiently well narrow down the sender and the recipient of a transfer. And it would not be good for users to be misled that they have a level of privacy that they don't actually consistently have.
Or maybe there is a way to go around the above, just can't think of any.
Here is an alternative approach, where computation is performed on encrypted data: https://www.openzeppelin.com/news/how-fully-homomorphic-encryption-enables-private-shared-state
Maybe that is a more promising path.
RE: River Whitepaper - A Privacy Layer for Hive