I'm trying to understand why you think it's bad that Taylor Swift tries to maximize her own revenue, but it's fine that Apple does the same, using her likeness and music to do so.
Honestly, when I first heard of the story (word of mouth) I immediately thought she was not understanding how it really worked. I had flashbacks to Metallica resisting streaming because they just didn't understand it. I thought there was no way Apple _actually_ wouldn't pay artists during those three months, so I dismissed it.
Then I realized she was right.
I wouldn't say I'm a Taylor Swift fan (at best, some of her music is fun to listen to with my teenaged niece) but the amount of ire some people have for a pretty person is just astounding. Yes, she's pretty. Yes, she sings about things that tend to be targeted at teens, especially girls. But those points don't change anything.
The letter accurately said, "These are not the complaints of a spoiled, petulant child." I have no idea how many people are behind her persona (I would guess it takes the equivalent of a small town) but I bet some of them had a stake in helping craft the letter. This was a business-to-business correspondence, even if it was written 'as a girl'.
At the worst, she's a logo for a company. At the best, she's actually got a pretty solid sense of business. Either way, she has a right to use her persona to make money.
Could be a bit of a stretch, and this note wouldn't be made public if she didn't sign off on it, but I think this is more measured than an artist just pushing for revenue.
When she previously removed her album from Spotify she implicitly let it be known what her motivations were: maximizing her own revenue, even if it was at the expense of other musicians. End of story. She would rather you give your $12 entirely to her instead of Spotify (or another album), which spreads it around. And I'm totally fine with that decision since she might seriously be the only musician alive with enough juice to get away with it. But the point remains that she's already made her motives perfectly clear, so when she wrote that letter to Apple it was purely about making sure she got paid during that three month trial. Of course, other artists will get to ride her coat-tails some, so she played up that angle and pretended it was a moral crusade. If she tells Apple, "Tell you what, take the money you'd pay me during those three months and distribute it evenly to everyone else." then I'd applaud her. Until then, she's a hypocrite going after more money.