The problem is when they render external websites and unsuspecting users think they are using the phone's web browser. That is something Apple/Google can have rules about without banning/restricting web views.
Android has these in-app browsers too, they may or may not be subject to this.
A lot of apps use webviews to render HTML, often in ways where you wouldn't even notice it's web content. Apps shouldn't use webviews to render external web sites but nothing in the APIs restrict them from doing so (recent versions of iOS have made it seem like they're heading in that direction but nothing concrete).
Easiest thing would be for Apple and Google to enforce this via denying app approvals. Would be a very interesting fight against apps this popular, though.
Obviously both Android & iOS let you open things in the default browser.
iOS has SFSafariViewController, which more-or-less corresponds to Chrome Custom Tabs on Android. These basically make a browser UI that is in the of the app for the purposes of multitasking/app-switching, but which is controlled by the browser. Devs can't inject code into these.
And both have WebViews, which let the dev do more-or-less whatever they want inside their own app.