On a desktop computer by far the most common "dApp browser" is MetaMask, which is merely a Chrome/Firefox extension. The mechanism is simply "a web browser" that gives the web page the ability (via some injected JavaScript object) to "request an Ethereum transaction be executed" (which costs money to do, and might even simply be the transfer of money). If it were possible to make browser extensions for MobileSafari people likely wouldn't bother making entire replacement browsers, as the experience is categorically worse.

Alternative browsers--built using Apple's browser--exist on the App Store; the issue here is that users are paying for something via a mechanism that isn't in-app purchases: Apple wants all payments in the world to flow through them, and so the idea of a decentralized payment future is incompatible with the App Store.