It appears that iPhone users tend to be very loyal to Apple technology overall and are unlikely to switch to the products of competitors. Why does that not make demand for iPhones price-inelastic?

You might be tempted to claim that it does, but remember: it is never optimal for the seller to operate on a price-inelastic part of the demand curve. Whenever demand is price-inelastic, the revenue will go up and the costs will go down if the the seller increases the price.