I understand almost all of the theory that has been built upon in quantitative finance is based on the normal distribution, and obviously you wouldn't want to throw all of it out the window on a whim but since stock returns are clearly not as normal as we like to believe why is it so uncommon to treat them as not being normal. For example, could you not as easily simulate a price process based on, say, a student T random distribution as well as a normal one? Looking at stock returns we often see that a student T distribution fits it better than a normal one so how come something like this is never done (at least I have never seen it done)?

Would is the biggest limitation that prevents us from going further with these ideas?