There seems to be a misunderstanding as to how the US gov't is using anti-competition laws in the case against Apple. I'm no legal expert, but from what I've read, the core problem is Apple's various platforms allow 3rd parties but, through Market Manipulation (limited API access, stopping legal and fair products from appearing in their stores, etc...), never actually allow for free and fair competition on said Platforms and as thus is liable to be sued.
Basically, you can summarize the lawsuit down to 2 points,
- Apple is using its platform to limit competition in unfair ways; if iOS and others were not open to 3rd parties, this really wouldn't be a problem
- Apple may not be the largest player per see, but its Market Power and Abuse of said power is an indication of Monopolistic behavior
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A good example here would be Amazon and Google. Amazon is not the only shopping website in the world (neither is Google for search), but they have a lot of Market Power. On their Platforms, they need to ensure that they don't unfairly promote their products at the expense of other competition. Basically, the competition must be fair when you have a platform (same thing with Microsoft, actually).
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Note: Gov't don't necessarily care if you're a Monopoly, what they care about is if you're actively abusing your enhanced Market Position to limit competition or promote your own products.
Another Note: The US gov't doesn't necessarily use anti-trust laws for the sake of consumers they use it to guarantee competition and a fair playground/market place with the idea being that with more competition, customers get better deals and better products
Another Another Note: The US gov't is not suing Apple for the Phones (they can't touch that since people are voting with their wallets there) they're suing Apple for their OS, and the rules being unfair on said OS
TL;DR: Apple is abusing market power in a way that makes it difficult for it to compete on its platforms. Apple may have built the best sandbox but so long as they're allowing others to play in that sandbox they need to make sure the game is played fairly, this same rule applied to Microsoft during their anti-trust lawsuit case. Windows is Microsoft's baby, but if Microsoft unfairly promotes its products at the detriment of other competitors, then it;s an anti-trust lawsuit (as simple as that).
Also published here.