This might be a valid plan, if you opponent doesn't fight for the centre at all. But in almost all games such a plan is either impossible or carries the risk of overextending.
It is true that pawn levers are important. Such a pawn lever might be the advance f4-f5 or c4-c5. But usually you only play a pawn lever at the side of the board where you are stronger and ready to exploit the opening of the position. Not just everywhere …
In my view it would be much more correct to state the building of an ideal pawn centre as a standard plan. But the "ideal pawn centre" consists only out of the e and d-pawn, both advanced two squares. And even the building of this modest 2-pawn centre is usually fought tooth and nail by your opponent.
[Event "Nanjing Pearl Spring Tournament"]
[Site "Nanjing CHN"]
[White "Magnus Carlsen"]
[Black "Veselin Topalov"]
1.e4 e5 2.Nf3 Nc6 3.Bb5 a6 4.Ba4 Nf6 5.O-O Be7 6.d3 b5 7.Bb3
d6 8.a4 Rb8 9.axb5 axb5 10.Nbd2 O-O 11.Re1 Bd7 12.c3 Ra8
13.Rxa8 Qxa8 14.d4 h6 15.Nf1 Re8 16.Ng3 Qc8 17.Nh4 Bf8 18.Ng6
Na5 19.Nxf8 Rxf8 20.Bc2 Re8 21.f4 Bg4 22.Qd3 exf4 23.Bxf4 Nc4
24.Bc1 c5 25.Rf1 cxd4 26.cxd4 Qd8 27.h3 Be6 28.b3 Qa5 29.Kh2
Nh7 30.e5 g6 31.d5 Nxe5 32.dxe6 1-0
Take this brilliant game as an example: On move 14 Carlsen creates the "ideal pawn centre", it persists until move 30, where is proves its power by advancing and initiating a deadly attack. There is even a pawn lever thrown in at move 14, which opens up the f-line for the rook. But Carlsen didn't try to just move his c,d,e and f-pawn forward. He created the ideal pawn centre, which controls a lot of squares and can at times advance with deadly effect. He used a pawn lever to open up lines for the attack. Every move had a purpose.