Curiosity...

The main drawback is that play by both sides is ridiculous.

You may want to research what is known as 'the stonewall attack' which uses the same pawn chain you erected with d4,e3,f4 and Nf3.

However, the exact line you gave is quite flawed, for example:
2.f4!?: not horrible but inaccurate because black can quickly play 2..c5 to good effect and pressure white, or alternatively play Bf5 early.More common is e3 and probably bd3, and only then f4. 2.e3 stops Bf5 because now c4 is very powerful.

2..e5?? an outright blunder, giving away a free pawn.

3.Nf3?? another blunder, dxe5 or fxe5 would have both given white a free pawn.

3..f6?? This does not defend the pawn sufficiently, white still has 3 attackers against 1 defender.

4.e3?? again ignoring the free pawn, 4.fxe5 fxe5 5.Nxe5 is winning for white.

In summary: White can play with this setup, but he should blindly play it against all black moves, especially moves such as e5 which simpy give away material.

About the free pawn and etc. I would like to point out that I just made a quick example to mainly show the idea of the opening. Because i obviously would have taken the free pawn, but remember, this is just an example board. But I must also thank you for giving me the name of it.

The idea of an opening, in the case of th stonewall clamping down on the e5 square is only relevant so long as it is followe consistently.

2..e5?? provides justification for whites last two moves, both guarding e5. If white refuses to take the pawn then the idea behind the opening becomes null.

Remember, an opening is played by both sides, not just by one. Also, even the most resilient 'system' openings can not be played in complete dogmatic, auto-pilot style. When a move appears on the board such as ..e5 it should be punished.