Storage space getting full, or becoming insufficient for the app Store to operate and download apps is the number one reason why iPhone won't download apps any longer. And that's because there is no one answer to it – there are several factors contributing to the problem, any one or a combination of them would result in your iPhone not downloading apps any longer. There is no straightforward answer as to why, suddenly, your new iPhone 13 won't download apps. Part I: Reasons Why iPhone 13 Won't Download Apps