Flutter: ページを pop() したとき initState() は動かない

import 'package:flutter/material.dart';

void main() => runApp(const MyApp());

class MyApp extends StatelessWidget {
  const MyApp({super.key});

  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      home: const MyWidget1(),
      routes: <String, WidgetBuilder>{
        '/mywidgeet1': (BuildContext context) => const MyWidget1(),
        '/mywidgeet2': (BuildContext context) => const MyWidget2(),
      },
    );
  }
}

/*
  MyWidget1
*/

class MyWidget1 extends StatefulWidget {
  const MyWidget1({super.key});

  @override
  State<MyWidget1> createState() => _MyWidgetState1();
}

class _MyWidgetState1 extends State<MyWidget1> {
  int myCount1 = 0;

  @override
  void initState() {
    super.initState();
    myCount1++;
    print('myCount1 was incremented to $myCount1');
  }

  @override
  Widget build(BuildContext context) {
    print('MyWidget1 was built');

    return TextButton(
      onPressed: () => Navigator.of(context).pushNamed("/mywidgeet2"),
      child: const Text('Push'),
    );
  }
}

/*
  MyWidget2
*/

class MyWidget2 extends StatefulWidget {
  const MyWidget2({super.key});

  @override
  State<MyWidget2> createState() => _MyWidgetState2();
}

class _MyWidgetState2 extends State<MyWidget2> {
  int myCount2 = 0;

  @override
  void initState() {
    super.initState();
    myCount2++;
    print('myCount2 was incremented to $myCount2');
  }

  @override
  Widget build(BuildContext context) {
    print('MyWidget2 was built');

    return TextButton(
      onPressed: () => Navigator.of(context).pop("/mywidgeet1"),
      child: const Text('Pop'),
    );
  }
}

# 初期表示時
myCount1 was incremented to 1
MyWidget1 was built

# MyWidget1 から myCount2 に push()
myCount2 was incremented to 1
MyWidget2 was built

# MyWidget2 から myCount1 に pop()
(なにも出力されない)

# MyWidget1 から myCount2 に push()
myCount2 was incremented to 1
MyWidget2 was built

# MyWidget2 から myCount1 に pop()
(なにも出力されない)