Which was what was proposed for the Severn. The problem is that at high tide what is in the reservoir cannot be higher than the outside level so no power. Tidal flow works both ways but there is a point where the levels are the same and, again, no power.
ISTR that there was a proposal for the Severn that required a second (empty) basin from the barrage to somewhere near the Devon border. This would be emptied at low tide and the main barrage filled at high tide. That way there was always a differential in level unless you had let too much water through too quickly. I think that the idea was that you could generate electricity quickly.
Took and awful lot of concrete though and the poor sods on the coast had the tide permanently out.