Doesn't it make sense to use words that mean what you're using them to mean?
By your logic I could use the term "apple" to describe apples, oranges, limes, and all other fruit because they all behave in much the same ways that apples do. But that's silly because there are differences between apples and oranges [citation needed]. If you want to describe both apples and oranges, the word for that is "fruit", not "apple".
Using a touchscreen is less precise than using a mouse. If the user is using a touchscreen, buttons need to be bigger to accommodate for the user's lack of input precision. So doesn't it make sense to distinguish between mice and touchscreens? If all you care about is "thing that acts like a mouse", the word for that is "pointing device", not "mouse".