Animation will not proper when list of animated widget added in stack in flutter?

In my code user can add animated widget dynamically by press button. Here is my parent class

class ParentWidget extends StatefulWidget {
  const ParentWidget({Key? key}) : super(key: key);

  @override
  State<ParentWidget> createState() => _ParentWidgetState();
}

class _ParentWidgetState extends State<ParentWidget> {

  List<Widget> animatedWidgetList=[];
  @override
  Widget build(BuildContext context) {
    return Stack(
      children: [
        ElevatedButton(
            onPressed:() {
              animatedWidgetList.add(AnimatedWidget());// this is important
            }, 
            child: ButtonWidget()),
        Stack(
            children: animatedWidgetList,
        ),
      ],
    );
  }
}

Now, AnimatedWidget() has simple icon and it is moving along path. It also contain AnimationController, Animation and its Listener.

Everything works perfectly as long as it clicks slowly. But whenever user tapping fast (10 tap/second) UI will confused and animation will not work perfect.

But after few time(1 to 2 seconds) everything will be ok.

ROOT CAUSE:

what happening here? AnimtedWidget() contains Listener.

_animation = Tween(begin: 0.0, end: 1.0).animate(_controller!)
      ..addListener(() {
        setState(() {});
      });

This setState(() {}) called many time in every second.

Suppose animation duration is 1 second and setState(() {}) called 10 times per second, than AnimatedWidget() rebuild 10 times per second.

And if animatedWidgetList having 10 element of AnimatedWidget(), than 100 time setState() called in 1 second

So How do I figure out this ?