That's not correct; the opposite would be more accurate. Mozart wrote the majority of his music for the private enjoyment of patrons, and only towards the end of his life did he take a very big risk and try to live solely off compositions for the public (operas for the most part). Haydn spent most of his life as a servant at the court of Prince Nikolaus of Eszterhazy and was not allowed to write anything which would be performed outside the palace first. Modern composers, however, have to have some kind of public-spirited clause to get commissions from arts funds, or else make their music commercial enough for it to sell to the public.
Again a rather specious argument. As I said before, Mozart was considered modern, even advanced, to most audiences of his time. In addition Mozart's music contains many subtleties that are not readily apparent without careful study. The overture to Haydn's The Creation certainly doesn't sound traditional and direct (in fact it could have been written 200 years later), whilst on the other side something like Schoenberg's Five PIeces for Orchestra is anything but subtle and uses very clear, almost mathematically logical methods. The underlying technical principles are the same in all music, it is simply the surface style and other essentially superficial factors that change.