I think I should point out here that what you're describing is a doctrine of the role of naval power which is inherently biased towards the role of the stronger navy. If a navy is weaker than its opponent then it cannot expect to exercise sealane control and sealane denial, but what it can expect to do is contribute towards the winning of the war by interfering with enemy sealane control.Not sure if there was much Riverine Warfare in the ARW. In the ACW the USN definitely had the upper hand. At no time during the ACW did the CSN do what a navy is supposed to do which is protect merchant ships and the coastline from enemy attack as well as interior waterways. Commerce raiding has its place but it doesn't win wars.
The CS Navy was involved in protecting their coastline and interior waterways at many points during the ACW, such as the Virginia denying the James river to the Union in March-April 1862 and the Palmetto State and Chicora interfering with the blockade of Charleston; the latter was unsuccessful but they did materially aid in preventing the Union from capturing Charleston. Other Confederate ironclads (such as the Richmond) helped to prevent the Union from gaining control of waterways, though obviously they couldn't protect waterways they weren't in (this is the advantage the Union had from being able to control the seas).
The commerce raiding, meanwhile, caused massive economic damage to the Union along with forcing the dispersal of lots of USN warships. This materially delayed the effectiveness of the blockade and the economic damage would have been a factor if the CSA had ever managed to get a peace from the USA.
Given the near impossibility of the CSN obtaining naval superiority by strength, it seems gauche to say they didn't do "what a navy is supposed to do" when the reason for that is obvious. They did however contribute towards the war effort, both on the operational scale and on the strategic scale.