Why not 3. f4 in the Englund Gambit?

I'm wondering why 3. f4 is not the mainline in the Englund Gambit, and what's the follow-up:

As for the followup, black should continue in gambit fashion with 3 ... f6.

• 4 exf6 Nxf6 - black has plenty of development for the pawn and should be good with the tactics. If black gets in 5 ... d5 then it's a reversed Blackmar Diemer Gambit where white's extra tempo is wasted on the bad move f4. White could try to stop ... d5 with 5 c4 but that's another weakening pawn move, simple development with 5 ... Bc5 , then ... d6 and ... O-O etc. should be very good for black.
• 4 Nf3 fxe5 5 fxe5 - white's extra is doubled and weak, black should be fine with positional play. The plan is to recover the forward e-pawn and leave white with an isolated e-pawn on an open file.
• 4 e6 dxe6 5 Qxd8+ Kxd8 (or Nxd8) - white returned the pawn and black has easy equality, but in fact this might be white's best option.

On the 3rd move white has several ways to get at least a slight edge, and 3 f4 doesn't accomplish that, that's why it's not a main line.

Edit: I put it in an engine and 3 f4 is more interesting than I thought. Stockfish doesn't like my 3 ... f6 4 Nf3 fxe5 5 fxe5 line for black. So maybe it's that the main lines were decided by humans long before engines arrived on the scene, and in a theoretical backwater like the Englund nobody bothered to update the main lines.

When you move your f pawn the king is weakened... and that weakness is permanent. Your opponents response should aim to open up the center. The Englund gambit is already good at doing that... as white you're playing into blacks hands with that move. You also don't need to play f4, since you can force a concession by just defending the pawn with pieces.

You don't need a precise response to a move like that unless it's common in the database. Otherwise you should just respond to it conceptually, in this case by opening up the center and developing as rapidly as possible.

Now, the engine doesn't evaluate it as objectively bad, but that's because the Englund gambit sucks. Still, relative to the other options f4 is extremely bad. But the precise engine eval of the move doesn't matter very much anyway, since f4 is a long term weakness and over time you're just going to be more vulnerable no matter how well you play the opening.

3.f4?! d6 looks fine for Black.