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A couple drawbacks that I see:
1. white has no "3 - pawn" structure to nicely tuck their king behind when they go to castle.
2. Black can play e5 like you mentioned, which not only provides black with a nice opening, but also a "3 - pawn" structure on their king's side.

I believe that White's problem in your line is related to the pawn on e4, since 4...Nc6 threatens to win a pawn. White usually needs to compromise by playing d3 or Bd3. Black will get a comfortable position with g6 and and Bg7.
I don't think 4...e5 is such a problem, since it cramps Black's position and White will have a better d4-break.