The fact that so many books still name Mozart as "the greatest or most significant or most influential" classical composer ever only tells you how far classical music still is from becoming a serious art. Jazz critics have long recognized that the greatest jazz musicians of all times are Duke Ellington and John Coltrane, who were not the most famous or richest or best sellers of their times, let alone of all times. Rock critics rank the highly controversial Velvet Underground over rock musicians who were highly popular among teenage girls around Europe. Classical critics are still blinded by concert hall success. Mozart is played more than anyone else (not true, by the way), therefore he must have been the greatest. Jazz critics grow up listening to a lot of jazz music of the past, rock critics grow up listening to a lot of rock music of the past. Classical critics are often totally ignorant of the classical music outside the top 40, they barely know their lesser known pieces. No wonder they will think that Mozart did anything worthy of being saved. In a sense, Mozart is emblematic of the status of classical criticism as a whole: too much attention paid to performance and score worship (be it symphonies or Wagner) and too little to the merits of real musicians. If somebody composes the most divine music but no maestro picks him up and performs his music in a concert hall, a lot of classical critics will ignore him. If a major symphony orchestra picks up a composer who is as stereotyped as can be but launches her or him worldwide, your average critic will waste rivers of ink on her or him. This is the sad status of classical criticism: classical critics are basically publicists working for major labels, orchestras, and opera halls. They simply highlight what product the music business wants to make money from.
Hopefully, one not-too-distant day, there will be a clear demarcation between a great musician like Hans Rott, who was never performed much, and products of social circles like Mozart. At such a time, classical critics will study their classical history and understand which artists accomplished which musical feat, and which simply exploited their social circles.