I think Limpinhitter is spot on.
Completely agree with his analysis of the different eras.
How prior to the 70s a player didn't have to make a choice, because conditions (basically small-headed wooden racquets) allowed the great "big game players" to be successful everywhere, playing that same style on all courts.
Then came Vilas and Borg with a new extra-top-spin game, that was later developed and perfected with bigger graphite racquets, and then during two decades (80s and 90s) a player had to make a choice. The "big game" was no longer able to win on clay against this new especialized clay game (extra-top-spin, SW and W grips, bigger graphite racquets) though it was still able to win on grass and faster courts.
During two decades, if a player wanted to win on all surfaces, then he had to change drastically his game from one tournament to the next. Borg was able to do it (serve-and-volley on grass, absolute baseliner on clay), Lendl tried to do it and came close (Lendl also serve-and-volleyed on grass).
Other players changed their game very little among different surfaces, and still were close to win all the big titles on all surfaces: McEnroe, Edberg and Connors for example.
Agassi was the only one that actually was able to win them all (when they still were completely different and there were players specialized on different conditions) and in fact he didn't change drastically his game to do it, he was another genius that was able to play "his game" succesfully everywhere.
But later on, with homogeneous slow conditions and poly-strings, in the last 15 years "everybody" plays like a claycourt specialist with enhanced equipment, and once again, a player doesn't have to make a choice anymore: this type of game is enough to win everywhere (if you are the best one at this unique style).
There is a reason (and that is why Limpinhitter is spot on) why prior to the 70s there were several players (often playing at the same time) that were able to win many big titles on all different surfaces (Kramer, Gonzales, Rosewall, Laver, Hoad....), then during two decades that was almost impossible to achieve, and then during the last 10-15 years it is often the case that the very big players win big tournaments on all surfaces again (Federer, Nadal and Djokovic).
Conditions (not only surfaces and balls, but also equipment, type of racquets and strings) determine what happens in a given era.