To the best of my knowledge, there had never been a comprehensive study made of how accurate the predictions of strong players about the future of chess turned out to be. Surely Michael Botvinnik's prediction - made to Shachmat be'Israel ["Chess in Israel"] magazine in 1990 (Vol. no. 4, Dec. 1990, my translation from the Hebrew) - is one of the most accurate:
Q: Who of the young players in the top of world chess -- Gelfand, Gurevich, Short, Spielmann, etc. -- have a chance of risking Kasparov's crown?
A: It's hard to name a specific name. Of the young I must mention Ivanchuk, who is 21 today , and Gelfand (who is 22). Gurevich is too old -- he has no chance of becoming world champion. Of the youngsters who are still not known well enough, I must mention Vladimir Kramnik, now 15. He recently won the European championship qualification tournament, when all his opponents were older than him... we can also mention Shirov, who is now 18... In the west, Short is a great talent, but his character isn't sporting enough... I must also mention the Indian plater Anand, who has a unique playing style. His main problem -- he plays too fast.... if he gets better in this respect, he has a great future.