Weird things occur when setting and unsetting a DateTimePicker value

Select::make('status')
    ->required()
    ->live()
    ->options([
        'draft' => trans('Draft'),
        'published' => trans('Published'),
    ])
    ->afterStateUpdated(function ($state, Set $set) {
        $published = ($state === 'published') ? now() : null;

        $set('text_published_at', $published);
        $set('non_native_date_published_at', $published);
        $set('native_date_published_at', $published);
    }),

TextInput::make('text_published_at'),

DateTimePicker::make('non_native_date_published_at')->native(false),

DateTimePicker::make('native_date_published_at')->native(true),