A coated Pantone® sample does look different than an uncoated Pantone®. I guess if you'd never seen it in person that this might be hard to imagine. If you can get your hands on an actual color book you'll see why that is.
"Printing on uncoated stock generally requires more ink because the
stock is more absorbent. If you have a look at ink sellers, you will
notice their ink estimator will give you different results for the
same quantity of prints; less ink for coated, more ink for uncoated."
Because they do not produce the same measured color.
The aim of your production tool is to simulate what happens on paper. Computers deal with facts so approximately is not the same. Without this info the simulator can not produce an accurate simulation. (wheter or not your monitor can do this is irrelevant. If the system does not have this info then it can not even begin to serve its purpose)
The problem is, that they are actually the same ink, they're just labeled differently so as to afford having a more "accurate" preview, with the assumption being that everyone will always use the correct ink/paper, and that there will never be a need to do a read-across or use two different stocks in a particular job. The correct thing to do would be to have page layout programs which would require one to specify a paper, then simulate overlaying it with ink, and select an RGB representation based on the combination of those two properties.
I miss Cerilica's Truism (which was a page layout app which worked thus).