Tonalism is just one of many tools that modern composers can utilize in their work. The influences of the 1st Viennese School, as they are called, were many. Here is a small list:
1. Form - Sectional forms were refined to a great extent by Haydn, Mozart, and Beethoven. Sonata Allegro Form also was expanded upon by these three.
2. Thematic Structure - It was through the work of these three composers that late concept of the motif, leitmotif, and theme were refined and eventually established. Later composers, such as Wagner and Berlioz, expanded these concepts. Setting up matrices for serial composition also sets up the motivic structures within the work - these motivic structures are then developed utilizing many of the conventions established the 1st Viennese School. Again, as others have said in other threads, the Second Viennese School considered it's work as a continuation of the tradition and not a total departure.
3. Thematic Development - The means at which themes, motifs, and leitmotifs were developed was largely expanded by these three composers and then further expanded during the Romantic period.
These are just three of MANY different contributions made by Beethoven, Haydn, and Mozart. One important thing to consider when looking at influential marks of earlier composers in later composers work is that harmonic language has constantly been evolving since about the 11 Century AD. Thus, when you hear a work of Mozart and then hear a work of Stockhausen that echoes back to Mozart... you're not going to notice it harmonically.