I haven't seen it mentioned here in quite this way, so I'll give yet another reason.
If you leave your leadership position for too long, to go on a quest, you create a vacuum. Your internal and external rivals will take advantage of it. Things will collapse because you aren't there to manage it. Or things won't collapse (a sign of choosing good underlings) which only indicates that YOU aren't needed.
this is yet another reason why managers avoid taking LONG vacations. If you're gone too long, the organization will prove it can survive without you AND somebody else will step up to take your place.
So there is already a reluctance for a leader (high level NPC) to get into long quests that aren't directly within their domain. Giving the PCs some assistance makes you lookk good, but doesn't put you at risk.
Add to that resource constraints. if the town sheriff takes all his men to root out a goblin cave, the town is left unsecured. Whereas, he can convince the adventurers to do it, AND he can claim success at helping that effort AND securing the town.
Couple in the fact that at each budget meeting, he's trying to get more money and men. If he just does the quest AND nothing bad happens in town, he's blown his justification. If something bad did happen, he's fired for not doing his job. His safest bet is to encourage adventurers to do it and then use the argument of "if these adventurers hadn't stepped in, we'd still be threatened by that goblin cave"
Its not about evil politics even. A good leader has these same issues in a good environment. If he isn't careful, he will lose his position, and not be able to solve the problems he's been hired to solve. It's a catch-22.
The real point is, a NPC leader is hired to do a job. Solving problems for the PCs may NOT be in his domain of work.
As for problems that ARE in his job description, you'll have to work with reasons that justify him needing the PCs help. if the PCs discover a murder victim and they take it to the NPC murder investigation unit, if you want the PCs involved, you need to make the unit NEED the PCs help. The reason will likely be custom to your campaign and situation.