Sure, a silver sword can be used to kill a human, it's a sharp blade, after all. Many objects can be used to kill someone if you use them correctly, it's just that most aren't practical for that purpose. The thing is you wouldn't want to make a habit of it since it risks damaging a weapon that fewer and fewer people know how to make or repair. And sure, steel can be used on monsters, the Order of the Flaming Rose made its name hunting monsters with conventional weapons. But again, it's a matter of effectiveness. Many of the monsters carry some sort of magical property in them due to how they came into the world of the Witcher, and silver has some sort of magic property in its own right. The idea obviously comes from how many kinds of monsters in our own stories were traditionally susceptible to silver. Neither is completely useless against a certain type of enemy, but each has its own intended purpose.
Also, it is worth noting that we're dealing with a video game. Games are big on using X in reaction to Y. Use the shotgun at close range, use a certain combo to break a shield, etc. It adds an element of strategy to various scenarios because you have to determine the most efficient method of dispatching an enemy. Things start to get dull if the same thing works in every situation.
