First, she is hugely savvy and understands humans - certainly way better than most other Kami-sama and even most humans. She is the smartest and most complicated character in this manga. She very obviously has some goal in mind with Goro and Kogane and is doing whatever it takes to get there even if it's painful in the short run.
Second, Zanma-sensei is very familiar with how business works (for good and bad), and what Mogami is doing this time is pure corporate negotiation tactics. She is not the goddess of the larger Tokyo area (or anywhere near it), so she can't make direct demands of the Kami-sama for the area nearby where Goro lives. Pretend she's a CEO from a corporation in Okayama and that other Kami-sama is CEO of another corporation, though they're both in the same conglomerate of all the Japanese gods. Or pretend they're governors or mayors, but this manga is obsessed with corporate stuff.
What she did here is stick and carrot, 'making friends', then carrot and stick. In the last chapter she called up and the 'secretary' was obviously frazzled once they know who she was because bad stuff just went down in their ‘corporate’ territory. And while Mogami is from another 'company' she's got some pull as a CEO (and they're in the same conglomerate), and the secretary has to respect that. So Mogami was a bit 'tsk tsk' - but then turned it into neutral discussion for page 1-4 which got the secretary to feel they're in this together and admit some organizational failures. Then on page 5 Mogami explicitly says she's 'not out to blame anyone' (which is a lie), but this relaxes the secretary, and then page 6 Mogami slips in a request (set up the barrier) and then hits them with 'Oh hey, I didn't see any of your divine messengers who were supposed to be patrolling.'
At that point the secretary is rattled and admits some corporate failings (which would normally be unthinkable), so Mogami thanks them and then 'I sure am glad I did not have to bring the hammer down' (also to chase off the pickup guy, LOL). She then explicitly tells the secretary to give her thanks to the other Kami-sama, which means everything discussed here will come to light. So she will get what she wanted all along, which is for the other 'CEO' to kick the ass of his lazy 'employees' to do their jobs and patrol Goro and Kogane's area. That (and the presumably expensive big barrier) was the entire point of this call! But she knew that if she just called and asked directly she'd get the usual corporate runaround of 'oh we'll certainly take a look at that kthxbye!'
So there you go. Basically I <3 Mogami and don’t want people thinking she’s being totally random or crazy. But she is quite the manipulator, and I sure hope she’s ultimately on the side of good (fox wives). Again, this is all my opinion, but sadly I’ve seen these tactics before. Thank you for indulging me in this wall of text!
