Linux is trademarked as well. Is Linux a competitor to the iphone?

Yes. https://en.wikipedia.org/wiki/Linux_for_mobile_devices

Imagine you're an Apple lawyer, and you're explaining to the regulators that you are facing serious competition. You gonna send them that link?

I didn't say Linux was especially good competition for iOS.

But unless you can demonstrate that it sucks because Apple is doing something which qualifies as restraint-of-trade, which I would suggest is obviously not the case, that doesn't matter.

It actually does matter if it has no practical bearing on Apple’s market (most easily seen in pricing) power.

Theoretical competition is not sufficient to demonstrate absence of a monopoly.

It's not theoretical competition. It's actual competition, which is bad. These are not the same thing.

The doctrine that it's your fault if your competitors suck makes no sense. It's weaponized tall-poppy syndrome.

That's not the doctrine.

The doctrine is that you can't exercise monopoly power in certain ways. Monopoly power is an empirical question, and does not turn on merely whether it is possible to describe a market in which another product exists, but whether that is a real market in which the products are in fact competitive.

But even if you have monopoly power, if you aren't illegally exercising it, you aren't in trouble. So you aren't punished for being an empirical monopoly.

You're correct, it is a brand. The point stands though. Comparing "Apple" to "Android" does not work. Perhaps a comparison between iOS App Store and Google Play Store would be more apt, but that is another discussion.