Philidor Defence Move Order

It seems to be de rigueur (ooh, fancy!) to get into the Philidor via the "Pirc" move order - d6, Nf6, Nbd7, e5 - rather than the "traditional" e5, d6 move order.

What are the main reasons?

Obviously, 1 ... e5 opens the door to the alternatives to 2 Nf3.

But the Pirc move order allows 4 f4.  (Or, if you play 3 ... e5, the exchange of queens.) 

Is that basically it? People would rather risk 4 f4 than KG/Bishop's Opening/Vienna?

This is Lion variation of Philidor coming from the Lion defense.  The reason is the relative popularity of that Lion defense. 

Possibly helpful:
A Cunning Chess Opening for Black by Sergey Kasparov (2015)
http://www.jeremysilman.com/shop/pc/Cunning-Chess-Opening-for-Black-A-76p3899.htm
https://www.newinchess.com/media/wysiwyg/product_pdf/9008.pdf

The Black Lion, 2nd Edition by Jerry van Rekom & Leo Jansen (2009)

https://web.archive.org/web/20140627070118/http://www.chesscafe.com/text/hansen37.pdf

https://web.archive.org/web/20140627122350/http://www.chesscafe.com/text/hansen123.pdf

Play 1...d6 Against Everything
https://www.newinchess.com/media/wysiwyg/product_pdf/9051.pdf

[Edit: Post updated with @JamesColeman 's input, thank you!]

Using the Pirc / Lion move order, White ends up playing e4, d4, Nc3 and Nf3.  Using the regular Philidor move order, White is not obliged to play Nc3, and he can use that tempo in a more productive way.

iirc, After 1. e4 e5, 2.Nf3 d6 3.d4, Black can try :

3… exd4, the Open Philidor.  If Black wants to play this position, he’s fine.

3… Nd7, the Hanham line, which I believe runs into 4.Bc4, and White reaches a comfortable position (with loads of potential traps for Black).

3… Nf6, the … I don’t know if this has a name, but 4.dxe5 Nxe4 5.Qd5!, and again White has a comfortable game.

None of these variations are losing or anything, but if Black is looking for the popular set-up where he can play h6 and g5 and put his Knight to f4 (Nb8->d7->f8->g6->f4), he isn’t getting it through this move order.

 True, by playing the Pirc move order, White is not obliged to play Nf3, and Black has to deal with other possibilities. The consensus is, though, that Black can reach a fighting position in lines with early f4 or g4, positions he can fight for a win in a messy position, and this preferable to the slightly worse, slightly passive positions he gets from the Philidor proper.

My theory is rusty, so someone else may chime in with an improvemtn or move-order nuance, but I believe this is the reason.

Thanks SmithyQ for such a detailed reply. Certainly that 9 move line is better for white.    

I'd probably go for DeirdreSkye's move order - on the basis that, if I'm going to play the Hanham Philidor, I must believe I can out manoeuvre opponents. So queenless middlegames should be nothing to fear.

I gave some analysis and thoughts about the move order for black here,  #45 :

https://www.chess.com/forum/view/chess-openings/philidor-defence---help-me-learn?page=3