Yes, it also ignores that price is only one of many factors in the market - doesn't matter to some consumers how cheap your widget is if my widget has new tech/

Yes, it also ignores that price is only one of many factors in the market - doesn't matter to some consumers how cheap your widget is if my widget has new tech/features not found in your widget and consumers need those features. So company A in the example could drop prices and still not be able to compete with the superior product from company B. Happens all the time in the real world.