Agreed. (That may not be surprising.)
Overall, I prefer check-based systems (eg Circles in Burning Wheel and Torchbearer; Streetwise in Classic Traveller) but also enjoy resource-based ones. But I also conceded that, in most versions of D&D, stuff like the helpful sister will probably be done via free roleplaying and negotiation, rather than via expenditure of resources or making a check with a meaningful consequence for failure. I still think this is viable, and that claim is based on the experience of handling it via freeform roleplaying and negotiation in Rolemaster.
Part of what makes freeform approaches viable is that, in the end, the players will confront a challenge or obstacle or demand that it's clear can't be resolved by their PCs' helpful relatives or friends: eg if it's established that the mayor is neither relative or friend; and it's the case that the players (and the PCs) want the mayor to do X; then the players are going to have to come up with some plan of persuading the mayor to do X (or replacing the mayor with their friendly doppelganger who will do X, or whatever other plan they come up with).
And credit where it's due: I'm really just reiterating here a point already made by
@Hussar.