First of all, let's face it, humans are a burden. The gods may need the humanity, but dealing with all those humans, is annoying. Each require too much attention comparatively to the amount of faith they provide. So not only does the "godchief" delegate into the seven lesser gods, but those delegate into a number of divine servants, which themselves coordinate other lesser ones, and so on. Even those directly worshiping the godchief are actually handled by some of its direct servants. It's not that the gods couldn't do it, but it's a lot of dull and boring work.
So they have a full administrative body of lesser beings counting the prayers they get from each of their believers, if they have a request, amount of time they have been worshiping it, if there are other people asking for the same thing, the last time they received the god's grace, if they are asking for something special or some mundane thing, perhaps even something they would achieve anyway without the intercession of the god, etc.
And then trying to be creative and get a proper action. This is a retributive religion, so they need to keep their believers happy by fulfilling their requests. Or actually, fulfilling enough requests of enough believers so they don't turn their back on the god. They don't need to fulfill them always, but enough times. Or at least to someone they will know about, so the god keeps its reputation of being kind to the people worshiping it.
In fact, the problem are humans themselves. A god could be willing to spoil their believers by granting them all their wishes. Problem is, even if they wanted to do that, they have believers with conflicting petitions. If you are the Love goddess¹ and have 45 suitors requesting the love of a single maid (and in exclusive for them!), you need to let some of them down.
Now, you may ask why would that higher god share the pantheon with the other seven gods, rather than having them as nameless serfs. The priests will tell you that in his infinite love to humanity, he chose to raise the Seven to that position, and that all of them agreed to divide between themselves all the aspects of the live, not due to rivalry, but as a way for better serve the people through by specializing in one aspect. Just as artisans specialized in one artcraft by guilds, so they could produce a better result [or a consistently mediocre one].
This specialization will indeed help the divine administration, since all requests of the same type will be fulfilled by the same branch (god), and petitions will already come sorted by god (more or less, there's always the weird guy directing their prayer to an inappropriate god, but they are safer to ignore if needed). However, a point you won't be told is that if humans had only one god to choose, should they become angry with it, that's a net loss of one believer. But with multiple gods, he would turn to the godchief requesting they override the lesser god. Or he could turn to the god of hatred and revenge. So you convert a no-win situation where the god needs to turn down many requests, to one where the rejection actually causes fervor to a different god. They then have complex schemes to pay certain worship units in exchange for having received new adoration as a result of the actions of another god.
Note as well that the actions of the gods from the believers point of view are somewhat arbitrary, which is a way to say they have their own agenda. The goddess of love would supposedly prefer the man's petition, repeated during his marriage to keep his wife, than the prayer from a herdsman to gain the favor of the hosts' wife. Right? However, giving her to the newcomer would a cause a war, making many people to remember their faith in the god of war. From which the goddess of love would receive a 10% commission for starting the war from the god of war (although she may be able to squeeze a little more, since he is in so dire need of believers), and having the loved one away will make many people to turn to the love goddess to keep their partners tied, too. After all, in peaceful times, humans tend to relax their ways and forget the gods, conflicts are good for the gods.
Which sheds a new light on why the priesthood, who has devoted their life to studying the gods and their actions, is so interested on maintaining the peace. They are not working for the interests of the gods as much as for protecting the humanity from them!
¹ No reason to be feminine, but it is traditional to consider it that way, and it is useful later to use multiple pronouns.