In the last 30 years of cycling, 20 riders were able to win at least a 3-week stage race (TdF, GIRO, VUELTA) and at least one "Monument" Classic 
(Sanremo, Flanders, Roubaix, Liege, Lombardia , World Championships). 

In the last 10 years, only CUNEGO (Giro, Lombardia), VALVERDE (Vuelta, Liege), VINOKOUROV (Vuelta, Liege) and DI LUCA (Giro, Liege, Lombardia) managed the feat. 

In the 90's, BUGNO (Giro, Sanremo, Flanders, World's), ROMINGER (Giro, Vuelta, Lombardia), BERZIN (Giro, Liege), JALABERT (Vuelta, Sanremo, Lombardia), OLANO (Vuelta, World's), ARMSTRONG (TdF, World's). 

In the 80's, FIGNON (Giro, TdF, Sanremo), ROCHE (Giro, TdF, World's), HINAULT (Giro, TdF, Vuelta, Roubaix, Liege, Lombardia, World's), MOSER (Giro, Sanremo, Roubaix, World's), SARONNI (Giro, Sanremo, Lombardia, World's), LEMOND (TdF, World's), KELLY (Vuelta, Sanremo, Roubaix, Liege, Lombardia), MARTENS (Vuelta, Flanders, World's), ZOETEMELK (TdF, World's), POLLENTIER (Giro, Flanders). 

It's easy to see how the number of riders able to excel at both types of events decreases over the decades. 
In my opinion, there are several explanations. 

The level of competition in the CLASSICS has increased steadily over the years, with more and more athletes aspiring for victory than in the past. This determined an exasperated specialization and finalization in training and racing calendar planning. 

The same happened for STAGE RACES, with specialists focusing their efforts almost exclusively to the preparation of the grand tours. 

Undoubtedly, the PSYCHO-PHYSICAL demands of a classic 1-day race are very different than those of a stage race, thus selecting those riders that are more suitable to violent efforts, rather than endurance and recovery skills. 

THE COURSE characteristics of Classic races changed very little over the years, while stage races (especially Giro and Vuelta) decidedly designed the courses in favor of light riders, multiplying the number of uphill finishes and extreme climbing gradients. 
This determined that riders suitable to stage races have been trying to reduce their body weight as much as possible, to the detriment of the absolute power necessary to excel in the Classics.