Alapin French - refuted ?

I have always been doubtful on the Alapin French 1.d4 e6 2.e4 d5 3.Be3 (diagram) despite Tim Sawyer's excellent book on it that appeared in 1995.

The reason for these doubts is the line 3...dxe4 4.Nd2 Nf6 5.f3 Nd5.
Black harrasses the white bishop, white has nothing else than defending it with the queen : 6.Qe2 (diagram)

Let's look at the black replies :

a/ 6...Nxe3 7.Qxe3
...a1/ 7...c5 8.dxc5 (=)
...a2/ 7...Be7 8.fxe4 (=)
...a3/ 7...Bd6 8.fxe4 (=)
...a4/ 7...exf3 8.Ngxf3 (=)
...a5/ 7...Nc6 8.c3 (=)

...a5/ 7...Nbd7 8.fxe4 (=)

b/ 6...Nc6 7.c3
...b1/ 7...exf3 8.Ngxf3 (=+)

...b2/ 7...Qh4 8.Bf2 (=+)

c/ 6...c5 7.dxc5 Qa5 8.c3 (=+)

So it seems that black gets the better game in the majority of lines. Maybe the quiter 5.c3 is better, but that is another story.