Analogies don't accomplish anything in basically all of the uses I've seen. People want them to serve as proof, but it's a lazy way of getting out of showing the validity of a conclusion.
Most people go into a new topic or new issue area with a basically neutral stance. They aren't looking to disprove the argument, nor do they even view it as an argument. Rather, they're thinking "OK, show me how this is relevant - tie it into my life and how it affects me, then I'll make up my mind based on my feelings afterwards" (in a far more subconscious way - basically nobody actually goes through these thoughts consciously). Analogies are your chance to do that. Get the right one and people associate your issue with something they already hold a positive position on. Get the wrong one and they just ignore you.
It's not without it's uses as a technique but you have to make sure the model the analogy constructs is, well, actually analogous to the situation you are modeling.
Analogies are an attempt to generalize an argument. Say we are trying to prove that "It will rain" is a valid conclusion from "If it is cloudy it will rain and it is cloudy". We can generalize this to "A -> B" & "B" -> "B", which you will recognize as an application of modus ponens from formal logic. Analogies try to use this power on fuzzier topics.
A normative principle like "We should build a new post office" are so abstract that they cannot be tackled head on (try defining "should" in the comments section and having no one point out a flaw to see why this is difficult). Because of this, we try to make comparison to other, seemingly similar, cases in an attempt to draw out the underlying logical structure. Because of this, I think they are a powerful and useful argumentative strategy.
If I were to argue that Apple's app store policies were harmful, then I would do just that. I would define terms, define the parties involved, show the harm and to which parties, maybe provide some examples, show which laws it violates, and maybe suggest solutions.
But I don't see why involving Cheerios at a brick and mortar retail store would help clear anything up.
I'm not versed in formal logic, but I believe it would be:
"A -> B", and I want to prove that "C -> D"
So I make the analogy that "A is similar to C, and B to D in some ways" thus then C -> D"
A lot of people will take this as a valid proof. But it has yet to be proven that A and C, and B and D are actually interchangeable.
Edit: To refer this back to the original argument, saying that the AppStore is like a brick and mortar store, and Cheerios is like Epic games is a nice analogy, but it can't possibly prove anything because they are just not the same thing.
What they may do though, is potentially align the reader's point of view with the writer's, but not necessarily towards the _right_ point of view, assuming there is one.