First, I'm not sure that Stefan Edberg and Boris Becker were generational greats...at least by my standards (i.e. one of the 10-15 greats of all-time). To the extent they were, the majority of Sampras' grand slams were earned after Edberg and Becker were at the top of their game. 13 of Sampras' 14 grand slams came after Edberg's last (1992). Becker was still pretty strong through the mid-1990s, but only managed 2 grand slam finals after 1991...well before Sampras' run of greatness. Courier was very good for about 3 years (making 7 finals from 1991-1993, but never made another)...I'm not quite seeing how he is listed in the same sentence with Edberg and Becker.
Second, I think you misunderstood my specialists argument. I think it favors your argument.
Third, you seem to ignore the elephant in the room, i.e. the changes to the playing surfaces and their effect on the game overall. You pretty much need to be an all-around/baseline player these days to compete at the grand slams. In Sampras' era, you could rely on your serve and win Wimbledon or the US Open. The changes have largely wiped out the specialists, which is why you have the great all-around/baseline players winning all the tournaments...not because of a lack of competition.