Has anyone come up with reasons to make this worthwhile for PCs?
As written it really doesn’t do much that a PC couldn’t do themselves - unless a group has not read the guide and have no points in charisma or diplomacy between them...
My players haven't used it yet but I think there are a couple situations where it might make sense:
1. The pc's are in hiding. Let's say - just hypothetically mind you :) - that the pc's recently killed some Dottari and want to lie low until their Notoriety dies down. Yet they need some information. Solution: send a team to get it. Example: is there a bounty/reward posted for us? "Are the Dottari looking for someone that looks like me?" - seems like a really perilous question to ask.
2. The pc's are not available. Two flavors here: a) the pc's are not in Kintargo yet want information from there Or b) the pc's are busy gathering information on X and Y but know they needed to deal with Z after that, so they send a team to gather info about Z.
I'd also probably let the pc's use the team Gather Info option to investigate something they missed with a blown Knowledge Local check. There's a specific action that substitutes for Knowledge checks but Local is kind of fuzzy. You can't ask random people on the street about the magical immunities of a Bearded devil but you can ask for a tavern that is popular with dwarves. I won't offer this to them - they would need to propose it. I like it if players think outside the box but I don't do it for them.
Mine wanted to ask for more information on the rumours already received. My interpretation is that there is not much else that can be discovered once they no the rumour other than by taking action themselves
The rumours are there to spur the players into action. There's really nothing more to learn from them without actually looking into them.
Let's take a look:
1) Lord-Mayor Bainilus didn’t flee to Arcadia - No one really knows. Anything the group hears is purely hearsay.
2) Looks like Thrune’s bringing public excruciations to Kintargo - But he hasn't done any yet so this one was probably started by Hellknights or Dottari that he brought with him having loose lips. Or, because Barzillai is known for enjoying excruciations, it could simply be people assuming he'll start using them.
3) Dottari guard towers are so full of prisoners now they’re keeping those they arrest in warehouses - Sure, gather information could prove this one to be true but it wouldn't really direct the PCs in any direction more than what they would already know from the basic rumour.
4) Been hearing strange noises around the old livery again - Gather information would confirm that there's weird sounds coming from there. If the group really pushes an ally of theirs (or two or three) is going to be attacked by grimples and possibly be killed. (And if they survive they likely never saw the grimples so don't know what attacked them)
5) The Thrashing Badger burned down a few nights ago - Yep, it did. Everything else in the rumour is super easy to confirm and looking into the Thrashing Badger doesn't show anything. Having NPCs investigate the other two likely end up with the people getting arrested or, at the minimum, chased off by dottari/hellknights
6) Shensen missing - Nothing more can be learned
7) Nox is half-devil - Hearsay and assumptions. Nothing to really be confirmed by anyone.
8) Gangs in Redroof/Temple Hill - Yep, Gather information can confirm that. Again, likely with NPCs being confronted if the group tries to push the NPCs to get too much information.
9) Someone's killing tieflings - If that's investigated by NPCs that NPC may be the next victim.
10) Fights at Clenchjaw's - That's easily verifiable. NPCs aren't going to figure out the reason that's causing them.