Oddly enough, the database I'm using shows 13. nd5 as both stronger and more common than 13. ne4, but do let me know what you come up with.
And "playable for black" is a low standard. Nobody's trying to show that the philidor is refuted, but you haven't convinced me that it sets white serious problems in obtaining an opening advantage, either from the practical standpoint (white's moves are all pretty natural) or the theoretical standpoint (I would take white without hesitation in most of these lines). Why would you personally play the philidor over mainstream sharp, fighting openings (dragon, french winawer) or less sound but significantly more trappy options (ruy lopez schliemann defense, french marshall gambit?)
This line seems reasonable enough, but I was really looking more at 13. nd5 after 12. ...b4 - I think that's far stronger. Any thoughts on that?
Also, to get terms clear, what would you deem sufficient reason not to play this line?
13. Nd5 does look interesting. After the exchange, White can always respond to ...Qa5 with Qd5 protecting the a pawn, etc. It's also an interesting move, because I don't recall seeing it in any theory, so practically speaking, if it continues the game "out of book" it could be strong. I'm going to try to do some analysis on it now and see if I can't find it somewhere.
Oh, as far as the line goes, I'm just trying to show that I think it is playable for Black. Of course White's position is fine and it's a sharp game.