I think hooks are important for module writers and DMs!
An adventure is the presentation of an unstable or meta-unstable situation where adventurers can make a big difference, the hook is what informs them of this, they know that it'll be worth their efforts to get involved. Most places in the fictional world are likely stable, the law is upheld (or completely absent), wealth is hoarded by the strong, the wizard remembered to renew the wards etc.
The hook says here is a weakness, and if you are the first to exploit it you can get rich. The dragon is missing a scale, the local government don't have enough manpower to deal with a bandit gang, the wizard is missing from the tower, the king has gone insane, etc.
Agreed that a good hook can do this. The vast majority of pre-written hooks do not do this in any meaningful way.
Also, I think your examples are more akin to what DP in thinking of in terms of rumors. I hadn't really though of these as being distinguishable before (except with respect to randomness), but upon consideration I think the way hooks are generally used and the way rumors are generally used are distinguishable.
Most hooks I see in modules are telling the players what to do. Join a caravan, find the missing person, return the McGuffin, escort the princess, etc. Person X asks you to do Y. Even T1's "you are broke and seeking your fortune" is like this. Essentially, "This is the adventure you are going on tonight." The hook tells the players what they must do, because they are "hooked". Whereas rumors provide information, and what the players do with it is up to them.
Let's say the Duke asks you to secretly deliver a letter,
unopened, to a particular address. That's a hook that tells you what to do to start the adventure, but it isn't really interesting. But if in addition to that hook, you hear a rumor that the Thieves' Guild will pay handsomely for dirt on the Duke, then the players have a choice, essentially, between two adventures. You have effectively turned the hook (according to my definition) into a rumor; delivering the letter unopened is not longer something the players are expected to do, it is now information about the Duke and what he wants you to do, and is only one of the available options.
When the players receive the information is also part of what separates a hook from a rumor. If the hook is a map that the players find/receive at the start of the campaign, without more information, then it is a hook, because it is a clear path to follow. But if the players find a map in the middle of an adventure or campaign, and are not compelled to use it, then it is a rumor.
So I guess a good hook is one that both tells the players what to do, but also gives a reason why the players might want to do it. Which can vary significantly from player to player. So, a hook plus one or more supporting rumors. "Go to the Tower and fetch me the Heart of the Elephant," is the hook, whereas "The Heart is likely in the High Priest's treasury... I care not for the gold or petty baubles, just bring the Heart to me!" is a rumor.
I guess ideally you want to have the rumors first. The players have heard that the Baron is a good man, who rewards loyalty, and that the High Priest is evil, and his Tower is full of riches. And then the Baron asks them to fetch the Heart.
So hooks are hooks, and rumors are bait, I guess? I'm sort of thinking out loud here. So, "guard the caravan" is a hook, and boring on its own. More interesting is, "The One-Eye gang keeps raiding my caravans, and has taken me for a fortune. Protect the caravan if you can, but more importantly, I want you to track the gang back to their lair, do what damage to them that you can, and report back. If you find my treasure, you can keep whatever you can carry on your person, as long as you tell me where to find the rest."
The stability of a situation is the difference between an adventure module and a setting module. Writing up a castle with its defenders and treasury and political entanglements is not much different than writing out the statistics and behavior of a monster, it's not an adventure but an element of a possible adventure.
I think a good setting
also has built-in points of instability. Say the Duke asks you to deliver the letter, and there is no specific rumor, but the players know that in-setting the Tyrants criminal gang pays for information, and decide to make a little money on the side. There is real pleasure when the players get to know your setting well enough that they start leveraging that knowledge.