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If we could land on an asteroid, not necessarily a human, we would save the fuel consumed for flying the spacecraft and we will benefit by having the systems on it running for a very long time..
If the selected asteroid is flying in much higher speed than our spacecrafts, we could get lots of info by its equipment for a very long time and even have it fly so far than any spacecraft have ever get.
Is it possible?
If the asteroid is moving at a "much higher speed than our spacecraft", then the spacecraft will either:
You'd need to spend fuel to match velocity with the asteroid to land safely, but at that point, you're on the same trajectory as the asteroid anyway, so landing accomplishes absolutely nothing. You can't land on an object that's moving much faster than you.
This would be like suggesting you can save gas by standing by the side of the road and jumping onto cars that pass at highway speeds - to not die in the process, you somehow need to get up to nearly the same speed as the car in the first place, which requires fuel.
The asteroid is on an elliptic orbit around the Sun. It does not need any fuel to keep this orbit for centuries and even millions of years. If the spacecraft should land on the asteroid it should match its speed and position very precisely to the asteroid. After this match, both the asteroid and the spacecraft will follow the same orbit without needing any fuel. It does not matter if the spacecraft contacts the surface of the asteroid or not.
If the asteroid is flying in much higher speed than our spacecrafts, it is impossible to land on it.
The Voyager spacecrafts are much faster than any asteroid and are leaving our solar system. Their distance to the Sun is increasing continually and they left any asteroid behind many years ago.
