They would have been very useful for the Union, and the Confederates were well aware of their value and weaknesses. To get to the main river of value, the Alabama, you had to get past the Mobile forts. It would only make sense to then take Mobile, before heading up the rivers. Two sets of batteries had been constructed above Mobile, one at Choctaw Bluff and one near Mount Vernon, to prevent river ascent, but they would have only worked if there had been a ground force to protect them from being cut off.
Up the Alabama River was Montgomery and river travel from Mobile to Montgomery was heavy and very important. It is unlikely that the Union would need to use this route to take Montgomery, some 250+ miles up river. Selma, with its railroad connections and iron works, was also up river, some 60 miles before reaching Montgomery.
The other river system was the Apalachicola/Chattahoochee River up to Columbus. This could have interrupted corn shipments to Richmond and destroyed the factories in Columbus, but again, you had a 250 mile trip to get there. Also, the lower reaches of the river were very shallow much of the year. In fact, there was no steamboat travel on the lower reaches in 2 of the years just before/early in the war.