The simplest, most honest answer is that we're cheap. Using the same size and kind of tire at both ends lets you rotate tires and extend tire wear. This can be really important on a front-driver that burns through front tires at least twice as fast as the rears. Running different kinds, or even different sizes at either end, would not only force more frequent tire changes, but also force you to deal with constantly varying tire conditions. Instead of keeping the front and rear tire wear relatively well matched through tire rotation, you would set up the car with fresh rubber at both ends and soon have a car with worn rubber in front and fresh rubber in the rear.
Of course, there are plenty of cars out there with different size tires at either end. And for those cars, there really is no excuse. Trying to choose optimum front and rear tires independently opens up a lot of opportunities, but it would add another huge level of complexity to the already complicated business of suspension tuning.
The best car I ever drove, a 2600-pound Bozz-tuned Evo VI, used the same tires on all four corners, but used different wheel widths to try and change the tires' behavior to match the unique needs at either end. The front wheels were slightly wider, squaring up the contact patch for more grip and sharper turn-in. The narrower rear wheels rounded the rear contact patch a bit, reducing grip and making the breakaway character smoother. I've never seen any tuner do anything similar before or since and I've still never driven another car that made me feel like such a hero, so I'd say it was probably a pretty good idea.
Pirelli actually designed a tire, the P-Zero Asimmetrico, that has different front and rear designs optimized for the different needs of front and rear tires on rear-drive cars. We've never, unfortunately, had any cars expensive enough for the Pirellis to even fit.