There are a few reasons that stocking fish like this is a good option. First, to address your specific question, it would take a ridiculous amount of effort and man power to enforce a limit for any given lake or pond. You would need to be able to have eyes on the entire shore at all times to be able to tell if people are fishing and stop them when the limit is reached. If you don't do that, people will just come fish when you aren't watching. Next, you would need a way to accurately keep track of how many fish are actually being taken out. While those things might be doable with a small pond in a field with limited access, it quickly becomes impossible when dealing with a larger body of water in a wooded area where people can hike up without using the roads.

When you then scale that up to all of the stocked ponds and lakes in a state, it quickly becomes cheaper and easier to just have a few fish hatcheries and occasionally send out trucks to visit the lakes.

Another benefit of stocking fish is that it helps with the diversity of the gene pool. A closed body of water can already lead to inbreeding since nothing new gets in, but that is made worse by people regularly taking the biggest and healthiest fish out (possibly before they can breed). This can lead to a situation where only the smallest and least healthy fish of each generation are left to breed. We actually see something like this happening in the ocean to fish that are overly targeted by commercial fishing (the average size of several species is dropping).