The entire point of the set up is that you are rewarded constantly, with small things, for exploring. And while you are being rewarded for exploring, why not get even MORE rewards by turning in the stuff you gathered while exploring?
You don't have to do those if you don't want to do them. They are repeatable quests that can largely be ignored. If you want more power or just to rank up the Inquisition, they can boost you a little, but by no means should be the main focus.
Sending out your advisors for resources should be a last resort, or ones you do while waiting for the multiple hour assignments. The way I use it is by only taking those assignments when I want a specific advisor for an assignment, but its already on one. So I send the others to get resources and when the advisor I want is free, THEN I come back to the War Table, and not any sooner.
I'm never low on resources unless I just crafted all new sets of gear for all 10 characters that are equipable in game. This isn't a lazy game, if you want everything to be handed to you without any time or effort, load up a game on your iPhone, give them your credit card number, and you're all set.