:"we can paint a picture and inform the reader at the same time by simply describing his many achievements"—that would not be a substitute for "considered by many to be the greatest chess player of all time", since it would need a comparison of Kasparov's achievements with those of just about every other recorded chess player. 
 :"For example, compare the above with the lead paragraph to Kobe Bryant"—that's just WP:OSE, and even if your argument were valid, there are also pages that have leads similar to the one in this article, such as Roger Federer and Lionel Messi.