Why is Bc4 ...Be6 bad for Black in Philidor's Defense?

In openings such as Philidor's Defense, Bishop's Opening, and Pirc Defense I commonly see beginners playing ...Be6 to challenge Whit'e's bishop at c4, but masters rarely play ...Be6. Why not? After Bxe6 ...fxe6 Black gets doubled e-pawns and exposes his kingside somewhat, but I don't see this is a fatal weakness, and one database shows Black surviving such a position, although admittedly White's win rate soars to 80%-100% at times.

Here's an example of such a beginner's game I mean, from this site in 2007:

https://www.chess.com/forum/view/chess-openings/anyone-know-what-opening-is-this

According to one database, after the above four moves, White wins 54% of the ensuing games, which is an unusually high percentage for that early in the opening (40% is roughly what I would normally expect for the first 4-5 moves of most sound openings).

If I continue along with the most popular line after the above moves, it ends with this position...

...with two games shown in the database, both with White winning.

However, with 10...Na5, the database also shows a drawn game between 2400+ players, so it must not be a certain loss.

For another beginner's example of this Bc4 ...Be6 situation, see post #2 at:

https://www.chess.com/forum/view/game-showcase/punishing-the-philidor

Black has bad dark squared bishop, weak king and weakness on light squares... 

Not fatal and not genial for black, first played by Tartakower in 1937:

https://www.chess.com/games/view/29174

3 reasons:

1) Black has just spent 2 moves that helps his light squared bishop.  Why trade it?

2) Black now has those pawns on dark squares impeding his bad dark squared bishop.

3) White will often work his queen to b3 attacking e6 and b7 simultaneously.  If a knight gets to g5 either the pawn at e6 gets attacked, h6 gets played (another pawn on dark square), or black's bishop goes to e7.  While all these ideas are defendable it is often not what black wants out of the opening.

It's supposed to be ok in the endgame - the king just sits next to the pawn and nothing can grab them

and not so great in the middlegame.

It may be safe for a draw but most players want an active defense with black that may give them winning chances.   And you have to get to the endgame through the middlegame. Good luck.