I don't think design is irrelevant to profits, but I also think tying it to Apple's position as the most profitable mobile manufacturer is weak. While Apple has competition, it is at the same time in a position where it's competition can't sell iOS phones. That gives it a substantial buffer against price pressure that none of the Android manufacturers face.
If you're agnostic to the OS, then, yes, Apple needs to convince you to buy theirs. But if you've decided on a platform - and design may certainly be part of that -, Apple has no competition, while every Android manufacturer is competing in an environment where people aren't only competing with unique devices but where they're also facing clones of clones of clones (e.g. my current Android phone is a Vernee Mix 2; Google recognises it as a Xiaomi Mix 2... there's at least half a dozen Mix 2 "clones" on the market, copying anything from just the exterior case to being near perfect copies including copying aspects of Xiaomi's UI)
So Apple has a much more sheltered position, especially as users get entrenched with large investments in apps and the overall ecosystem. Most of the Android competitors are competing in price segments Apple are uninterested in, but for most Android manufacturers at any price point has to deal with competitors selling phones that look and feel almost as theirs but costs 10% or 20% or 30% less - close enough to have near feature parity and attract the same customer segments -, which affects their margins substantially.
Couple that with Apple's logistics and manufacturing and integration and it's not surprising that Apple is so much more profitable.