You have completely missed the big picture here.
Google charges 'volume' users of their maps API, that is part of the way they pay for it. The map "application" on iOS was a client that called Google Maps APIs and displayed the results. It generates a lot of volume, and Apple was going to have to start paying for that this year.
you wrote: "For example if you show a map on your homepage with all the locations of your stores."
If you did that enough times Google would start charging you. They also reserve the right to show ads for somebody else's store on your map. (not that they would just yet, but they keep that right in reserve if you want to use their content.)
Google and Apple sell Ads. Google is much better at it than Apple is, but the great untapped market is effectively advertising to mobile users. A common theme for desktop users is they use web search a lot, a common theme for mobile users is that they use map search a lot.
Apple wants you to sell ads through their network, so they get a huge chunk of the ad revenue that you are getting for your content. They do this because you're showing your ad on an Apple device. When you use Google maps through a browser you get ads from Google's ad network on the page. If you use an Application (usually a better UX) the platform provider has more control over you (they have to approve your App after all) So the fight here is who sells the advertisement into the Maps data stream.
Google has the best mapping product on the planet at the moment. They can use that to demand concessions like "we get all the ad revenue" in exchange for you being able to use our data/api. They don't care if the local restaurant shows a map to their location, the do care if you're an application that millions of people might use.
Its pretty clear that Google and Apple agreed to disagree and end their relationship with respect to Maps. That the Apple product is so horrible suggests that this relationship ended earlier than Apple planned, or their Maps technology has matured more slowly than they anticipated. Either way, the result is that Apple now has a grossly inferior maps application on their most successful products. This is going to cost them both in sales to people who are on the fence with regard to mobile, and in customer goodwill (this is already evident). That is a calculated risk they took. The alternative was to meet Google's requirements, whatever they were, to continue to use their map data in their application.
The part I think you are missing is this. Apple had to know how crappy their Map application was, customer experience is what they do, they don't just forget about it all of a sudden. Given that they are shipping that pile of crap means that they and Google are at odds on this issue. Is there any scenario where Apple would 'approve' an application by Google that would be instantly significantly better than their native App? Or conversely, given that they couldn't reach an agreement on the native App, do you think Google would agree to constraints in a published App that they would not agree to in a native App?
No, the only explanation that is credible is that they walked away and Apple has dug in their heels and bet that they can build out a better map experience faster than Google can take market share away with Android's map experience. From where I am sitting, given the significance of the risk involved in taking that path (some of which we're seeing being actualized as rampant ridicule) I can only imagine how distasteful Google must have made it for Apple to stick with them. And that suggests to me that you will never see another native Google maps product on iOS until Apple capitulates and cedes the space to Google or Apple moves so far ahead of Google that they no longer feel it is a threat to their advertising base.