The weir actually provides a controlled release of water when TVA is not sluicing or generating. Granted that there is going to be some fish lost, but I think that it is better than having the river bed run "dry" without a continuous flow.
The weir on the Clinch reminds me of the salmon ladders that you see in Oregon, Washington state, etc. to allow salmon to travel upstream to feed, spawn, and do other things.
On the other hand, the weir dam on the SOHO prevents any fish from moving upstream between the weir and the dam discharge pool. Those fish are basically landlocked with no where to go.