Btw, the slams should be the barometer. Big tennis players like Sampras have always lived by it, they know the importance of it. Fans can have their own favorite, their personal opinion, but generally the tennis scene will accept the player with most slams as the best, regardless whether you think has the best style, most talent, whatever. It has always been like that and brought up regularly in GOAT conversations when Sampras and later Federer ruled this statistic.
Slams are where the big stars give their all and more, all the tournaments they play up to it in the run up are just to prepare them mentally and physically for the 4 dates on the tennis calendar each year. Especially for the big three the other tournaments have nearly been the equivalent of pre-season in football.
Just look at the consistency of the big three this decade and a half in grand slams. This very consistency (without googling I'd bet only 3 or 4 players other than the big three have won a slam in the past 10-15 years, probably less) proves the best rise to the top in these events, slugging it out over two weeks in best of fives (less chance of upsets as the better player has more time to come back) under more scrutiny and pressure. So naturally the one of the big three who come out on top in these events most is the best.
Grand Slams are set up to be the barometer of where a player's position and legacy is in this sport.