Casework is one of the main functions of an elected representative and is also an invaluable reelection tool for incumbents. It provides a clear example of how representative government operates by allowing the representative to get feedback on the performance of a particular agency while coming to the aid of a constituent. The other side of this coin is the obvious advantage it gives to an incumbent running for reelection.
However, it seems to work well for both the public and the incumbent: it incentivizes legislative action at the federal level, on behalf of the individual difficulties faced by members of the voting public, due to the possibility of getting more votes come reelection time.
Also, this type of legislative activity provides oversight: it acts as a check against administrative action.
Once a public administrator hands down a decision on some particular issue of concern to someone, that individual is generally left with no other course of action, the issue is settled. That individual could appeal to the courts, but such an appeal would likely be decided by administrative courts that are more favorable to administrative concerns.
In such an instance, where legal action seems impossible, legislative casework rises to its highest level of importance.
For it is often the case, that a few calls from the office of a congressman or senator will break bureaucratic logjams and sway decisions in a more favorable way.