Ionic is based on Cordova/PhoneGap which uses WebViews. I'll try to answer the more general part of what can you not do with hybrid apps or more exactly, example of things that seem impossible using a WebView:
- Replacing a DOM element with a native element is possible via overlays, but they cannot be attached to the DOM so if your element is animated via JavaScript or CSS it would lag behind (supposing you manually inform the overlay of its expected new position); scrolling should be possible to synchronize though.
- Cannot customize well for accessibility.
- cannot customize text selection / long tap.
- Another good (and frustrating) example is that on iOS you cannot remove the accessory bar on the keyboard. There are some plugins that can do it for certain versions of iOS, but it's super fragile and doesn't work 100% of the time.
As said, there are many things that are iOS-only or Android-only but those are almost always only because no one made the plugin for the other platform.