Flutter persistent navigation bar with named routes?

All of your 3 requirements can be achieved by using a custom Navigator.

The Flutter team did a video on this, and the article they followed is here: https://medium.com/flutter/getting-to-the-bottom-of-navigation-in-flutter-b3e440b9386

Basically, you will need to wrap the body of your Scaffold in a custom Navigator:

class _MainScreenState extends State<MainScreen> {
  final _navigatorKey = GlobalKey<NavigatorState>();

  // ...

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      body: Navigator(
        key: _navigatorKey,
        initialRoute: '/',
        onGenerateRoute: (RouteSettings settings) {
          WidgetBuilder builder;
          // Manage your route names here
          switch (settings.name) {
            case '/':
              builder = (BuildContext context) => HomePage();
              break;
            case '/page1':
              builder = (BuildContext context) => Page1();
              break;
            case '/page2':
              builder = (BuildContext context) => Page2();
              break;
            default:
              throw Exception('Invalid route: ${settings.name}');
          }
          // You can also return a PageRouteBuilder and
          // define custom transitions between pages
          return MaterialPageRoute(
            builder: builder,
            settings: settings,
          );
        },
      ),
      bottomNavigationBar: _yourBottomNavigationBar,
    );
  }
}

Within your bottom navigation bar, to navigate to a new screen in the new custom Navigator, you just have to call this:

_navigatorKey.currentState.pushNamed('/yourRouteName');

To achieve the 3rd requirement, which is Navigator.pop taking you to the previous view, you will need to wrap the custom Navigator with a WillPopScope:

@override
Widget build(BuildContext context) {
  return Scaffold(
    body: WillPopScope(
      onWillPop: () async {
        if (_navigatorKey.currentState.canPop()) {
          _navigatorKey.currentState.pop();
          return false;
        }
        return true;
      },
      child: Navigator(
        // ...
      ),
    ),
    bottomNavigationBar: _yourBottomNavigationBar,
  );
}

And that should be it! No need to manually handle pop or manage a custom history list.

CupertinoTabBar behave exactly same as you described, but in iOS style. It can be used in MaterialApps however.

Sample Code