Think about it, why would WordPress do anything just because you have defined additional class?
It’s not magic (neither magical magic or code driven magic). The text widget doesn’t appear simply because class exists. When WordPress loads it runs wp_widgets_init(), which executes register_widget('WP_Widget_Text').
So technically you cannot tell it to use different class. What you can do is unregister the native class and register your own. As long as your class outputs same name and settings it will be practically indistinguishable from native widget.
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