"
Economic output?Influence abroad?
Cultural contributions?
Trade hub?"
Yes, Yes, Obviously, and not as much.
At its height, Sparta was one of the more important military powers among the Greek city states. After the Peloponnesian war, which it won, it was for a time the dominant and most influential of all Greek city states. This dominance and influence is the reason that ancient Greek writers found them important to talk about and consequently is the reason we still talk about about them. The fact that we still debate the legacy of the Spartans speaks to the wide range of their influence.
""You know what? We'll give it a try but even if we do conquer Sparta all we'll get is a bunch of olives, goats, and a whole bunch of whacked-out weirdos with no gold, no navy, and a lot of baggage. So commit but don't 'Commit' and if we lose we'll just wait them out and color in the entire map later when they inevitably collapse." "
Actually, Sparta was quite wealthy if you measure it's wealth in productive farmland land rather than precious metals. We privileged modern westerners don't really recognize the importance of that, but it was quite important for the time.
Also, while the Spartans did not initially have a navy, they had no trouble buying one from the Persians and beat the previously unbeatable Athenian navy with it.
Olives were actually incredible valuable to the ancient Greeks (still are valuable, actually) one of the most important crops and essential to all of their industry. According to myth Athens was given the choice of naming their city after Athena or Poseidon. Athena offered olive trees while Poseidon offered naval power. The Athenians judged that olive trees would be more valuable.