Why isn't 5. f4 considered strong in the French Advance, main line?

Question

Why isn't 5. f4 considered a strong move in the main line French Advance, after

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1. e4 e6 2. d4 d5 3. e5 c5 4. c3 Nc6  

Everyone plays 5. Nf3 here, but isn't it logical to support e5 with a Pawn and later 6. Nf3, as it is for example in the Steinitz Variation of the Classical French, after

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1. e4 e6 2. d4 d5 3. Nc3 Nf6 4. e5 Nfd7 5. f4 c5 6. Nf3

Answer 1

After 1.e4 e6 2.d4 d5 3.e5 c5 4.c3 Nc6 5.f4, black can put white's center under pressure very quickly. For example, after 5....Nh6 6.Nf3, black is already better after 6....Qb6 or 6....cxd4 7.cxd4 Nf5.

In contrast, one of the main lines of the Tarrasch variation goes 3.Nd2 Nf6 4.e5 Nfd7 5.f4 c5 6.c3 Nc6 7.Ndf3. In this line, white has a firm grip on the center, while black cannot manoeuvre Nd7 to the outpost on f5.

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      1.e4 e6 2.d4 d5 3.e5 (3.Nd2 Nf6 4.e5 Nfd7 5.f4 c5 6.c3 Nc6 7.Ndf3) c5 4.c3 Nc6 5.f4 Nh6 6.Nf3 cxd4 (6...Qb6) 7.cxd4 Nf5