Nothingness: e4 is too vague what moved to E4?

A pawn. If in algebraic notation the piece that moved isn't indicated (either using a symbol, or a capital letter), a pawn was moved.

Now, you say "P-Q4" tells you exactly what was moved and where to, but I challenge that. "e4" in unambiguous. It's the white square, three square straight ahead of the starting square to the white King. But "P-Q4"? That could either be white moving to "d4" (the black square three square ahead of the starting square of the white Queen), or black moving to "d5" (the white square four squares ahead of the starting square of the white Queen).

Not to mention that descriptive notation allows moves like "KxP" or "Q-B4", which require knowledgement of the current position to know which move was actually performed. OTOH, using long algebraic notation, the move is always unambiguous, and never needs the current position to determine which piece moved from what square to what other square. "e2-e4" cannot be any other move than a pawn moving from "e2" (which is always the same square - regardless whose move it is) to "e4" (which is also always the same square - regardless whose move it is).

There's a reason descriptive notation only ever caught on in a few countries, and is even considered obsolete there. Virtual all modern chess literature from the past decades uses algebraic notation. Chess literature from many countries have done so for over 150 years.