For the same reasons that universities stopped teaching Fortran and Pascal: They've been replaced by newer, better alternatives.
The author might have had more luck finding Marx if he hadn't been looking for him in the Economics Dept.
And I think you can most definitely call a philosophy wrong, philosophers do it routinely! At its core philosophy is simply making good arguments, something that HN posters should be striving for. And while it's hard to "prove" a philosophy wrong in the sense one can prove that an algorithm doesn't work, you can certainly prove its arguments to be unsound.
There is the ongoing strict separation between "Continental" and "Analytic" philosophy, which is both relatively new and quite tragic. I will say that in a discipline like philosophy, which when it is at its best treasures subversiveness and independence just as much as entrepreneurs do, it's all the more important to read thinkers from different schools of thought. Hegel is not just any "Continental" philosopher but one of the most important pillars of the field
Sure you can. Philosophers do it all the time.
I read all three in political science classes. I think philosophy might be a dead academic discipline, at least in the US. Most of the big names seem to have moved to more focused disciplines; e.g political science and women's studies.
True, one will be a better Economist if he understands the evolution of Economic thought in the 19th century, but there is no reason to single out Marx for particular study by the average student.