Schubert and Chopin were third tier geniuses? Wow. The first was music's first lyric poet and in his song accompaniments paved the way for Romantic piano music and the latter virtually invented the modern pianstic vocabulary and was the most forward thinking composer of his time. Anyway Mozart actually did have problems getting a good position at court and Brahms never held one.
Concerning Brahms, almost but not quite. By the time of Brahms, the concept of court musician had changed. For a number of years, Clara Schumann had held the position of court musician at Detmold. What went on at Detmold was a winter music festival sponsored by the minor nobility of that pricipality, and Clara's job was to set the programs, hire the musicians and schedule the rehearsals. This is something that an artistic director at a festival would do today.
When the young Brahms came into the life of the Schumann couple, Clara put in a good word for Brahms, and for two years he was the "court musician" at Detmold. He was expected to write at least one piece for the winter festival, and for his two years at Detmold Brahms wrote his Serenades in D and A (Opp. 11 & 12).
So technically young Brahms did occupy a court position.
I really didn't want to get into the artistic ratings game except as an anecdotal comment because one man's Mehta is another man's Poissant, LOL.
Leni