There’s an API for an alternative browser engine to add a web app to the iOS home screen, but the app opens in Safari. This creates a disjointed user experience before and after installation: based on different features, user state, and preferences across engines.
Apple has argued against allowing non-WebKit engines to render home screen web apps on security grounds. However, the fundamental security requirements for home screen web apps are the same as those already enforced in ordinary web browsing, where pages from different sites need to be sandboxed and isolated both from each other and from the rest of the device.
It is conceptually straightforward for an operating system to delegate web app rendering to a third-party browser engine, and Android has done this for years. This should be enabled in iOS as well.