You cannot install an app on an iOS device, except from their store. Apple won't let you install an alternative store. Therefore their app store is a monopoly store, and should be regulated as such. (Is the argument being levelled against them.)
This is the problem.
Why isn't "the world" the smartphone market where there are plenty of options?
At a certain point in debates like this everyone ends up over-examining analogies to a point where it isn't useful. To be a useful parallel you'd need a world where you can only buy two types of car and each one only lets you go to one type of shopping mall, or something like that. My point is, that isn't how either the real world works or how smartphone app stores work, so it's a debate over nothing.
"the definition of world is too narrow" is a pretty weak argument.
There are two options, and one of them is provided free of charge by the world's largest advertising company.
The state of the smartphone OS market is so wildly different from the general-merchandise retail market as to render any comparisons meaningless.
So you can compare this to if you could only buy things at two different stores, each store has a hefty membership fee, and you were effectively locked into your decision for at least a year at a time.
For a more meatspace example let's say you own a car with full self-driving capabilities. Now, the manufacturer of that car also runs a chain of grocery stores. It would be problematic if the car refused to drive too a different store. "If you've already to decided to buy a Walmart car then Walmart is the only store that you can go to."
There's the obvious problem around apps and protocols. If you've been using them for a long time, your apps, their connectivity to each other, personal data etc is likely to be locked into Apple services & devices, or Google services & devices, in a way that is difficult or even impossible to move over (I know people with data they can only access now if they buy a license to apps they can no longer run).
More subtly, for example there was a recent article about how people in some places experience a social penalty if they aren't using iOS, because the difference is visible to others in terms of protocols used for instant messaging.
In my view, the great difficulty of switching and the penalties of switching mean that both Apple and Android ecosystems are, more or less, separate marketplaces, and each one has a strongly dominant player that should be subject to anti-trust measures.
Basically if you build a platform ecosystem, expressly design to lock-in users especially in ways that hugely affect their lives, that comes with responsibilities you don't have in a free and competitive marketplace where your users can switch with low friction.
It's not like people have to choose whether to exclusively shop at Walmart or Target, like they do with phones. Reasonable people don't own both an iPhone and an Android.
Such as Coca-cola (who even has to stock their own inventory), and those shops and restaurants that are at the front of every superstore location.
Imagine that you buy a DVD player at Best Buy. That's cool. Best Buy decides the markup, where it puts it, how much it puts in promoting it, etc. That's also cool. You are OK with giving the with 30 % of your DVD player sales. After all, shelf space, promotion, etc. isn't free.
Now, imagine Best Buy hears that you sell DVDs by mail. People are already buying your DVDs and you are shipping it to their door, so you don't feel that it's worth your time and effort to "sell" them through Best Buy.
Best Buy is not happy with this. They say that for ANY DVD for the DVD player in their store, NEED to offered in their store AND you need to pay the same fee for which you get placement, promotion, etc.
You don't want to sell your "Mail in DVDs" in Best Buys, you don't want or need them promoting your DVD, they will never touch, manage, offer support, etc. for these "Mail in DVDs", but you HAVE to sell them in Best Buy because if you don't, then they will just stop selling your DVD player.
In short, they are in the business of selling DVD players, but want a cut of all "Mail in DVDs" because your customers bought the DVD player through them.
This is what Apple wants to do for any app that offers digital content / experiences that might not want to use their services. How is that OK?
The questions are, do we want phones to be like video game consoles with a walled-garden marketplace, or like general purpose computers where the manufacturer does not exert control over the entire software economy. There are arguments for both, but I think the former stifles innovation.
Meanwhile Apple wants you to buy their $1000 phones AND wants you to pay an extra 30% for all software and digital services.