I notice that ECO (3rd edition, 1997) likes Black in that line; it gives 10. Bd5 Ne7 11. 0-0 Bc7 12. Na3 Rb8 13. Be3 b6, with a slight advantage to Black.  So Black is varying from a couple of Estrin games there.  I see another Estrin game where he played 10. Na3 instead of 10. Bd5, but ECO again thinks that Black can get a slight advantage, by varying from what Estrin's opponent did.  So I wonder where Palkövi et al take issue with that.

The real con is 1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.c3 Qe7 5.d4 Bb6 6.d5 Nd8 7.a4 a6 8.d6 Qxd6 9.Qxd6 cxd6 10.Bd5 (or with 8.a5 in between).
It is a line of Estrin, but nobody seems to know about it. I have played it 3 times with white and black is in big trouble. Though I must admit I lost one due to my blunderradar not working.

1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.c3 Qe7

It would appear that this move for Black has fallen out of favor.  It appeals insofar as it is a move from the classical era of chess, but it also has some independent merit: it points another piece at the center and it discourages the advance of the d-pawn: 5.d4 exd4 6.cxd4? Qxe4+  It also seems to be an example of the road (relatively) less traveled of late, and worth a look.
 
5.0-0 d6 6.d4 Bb6 7.h3 Nf6 8.Re1 doesn't look so bad for Black.

But it turns out that White needn't be so afraid of 5.d4:

5.d4 exd4 6.0-0 d3 7.b4 7.e5!? 7...Bb6 8.e5 d6 must be the main test, when White looks strong.  Perhaps 5.d4 exd4 6.0-0 Ne5 7.cxd4 Nxc4 8. Qc2 b5 9.dxc5 Bb7 is a better effort from Black?

Pros and cons of the early queen move?  I suppose I've answered my own question: the point of 4...Qe7 is to prevent 5.d4, which it doesn't, in fact, do.  Having said that, Black has other options:

5.d4 Bb6 6.Bg5 Nf6 7.d5 Nd8 8.d6 cxd6 9.0-0 d5 with 10.exd5 d6 surely looks pretty reasonable, too.

5.d4 Bb6 6.0-0 d6 7.a4 a6 8.Bd5 Nf6 9.Nbd2 was tried by Macieja in a blitz game against Sasikiran, but surely White can improve on Black's collapse in that game.  Presumably 6...Nf6 7.d5 Nd8 is a good place to start.

Thoughts?