Flutter - ListView inside on a TabBarView loses its scroll position

Question

I have a very simple Flutter app with a TabBarView with two views (Tab 1 and Tab 2), one of them (Tab 1) has

Answer 1

Output:

---

Code:

@override
Widget build(BuildContext context) {
  return DefaultTabController(
    length: 2,
    child: Scaffold(
      appBar: AppBar(
        title: Text("PageStorageKey"),
        bottom: TabBar(
          tabs: [
            Tab(icon: Icon(Icons.looks_one), text: "List1"),
            Tab(icon: Icon(Icons.looks_two), text: "List2"),
          ],
        ),
      ),
      body: TabBarView(
        children: [
          _buildList(key: "key1", string: "List1: "),
          _buildList(key: "key2", string: "List2: "),
        ],
      ),
    ),
  );
}

Widget _buildList({String key, String string}) {
  return ListView.builder(
    key: PageStorageKey(key),
    itemBuilder: (_, i) => ListTile(title: Text("${string} ${i}")),
  );
}