Well, of course, the point is to pick up the knight with 4.Qh5+ and 5.Qd5+, but this just makes things too easy on black. White spends 6 tempi just to zap his King's bishop and put his Queen on e4. Black cannot castle, but there have to be better things white can do with his time.
In response to your question about chessgames.com, they were surely taking transposition into account. The vast majority of the 1500 or so games must have been reached by 1.e4 e5 2.Bc4 Nf6.
If there exists a refutation of Aljechin's defense, it is not in the variant 1.e4 Nf6, 2.Bc4.
Black can, if he wishes not to enter the above discussion, simply play 2....e5 (Bishop's opening), which is sound.
I don't see a problem in taking on e4, either: 2....N:e4, 3.B:f7+ K:f7, 4.Qh5+ g6, 5.Qd5+ Kg7, 6.Q:e4 Nc6, 7.Nc3 (otherwise 7....d5) e5. Black has a good center, and the bishop pair.
Exchange variation: 1.e4 Nf6, 2.e5 Nd5, 3.d4 d6, 4.c4 (or 4.Nf3 g6, 5. c4, or 4.Nf3 g6, 5.c4) Nb6, 5. e5:d6, and now both c7:d6 and e7:d6 give white a pleasant game (more space, with no weaknesses).
I believe, also the following Bc4-variant is very good:
1.e4 Nf6, 2.e5 Nd5, 3.d4 d6, 4.Nf3 g6, 5.Bc4, and now, for instance,
5....Nb6, 6.Bb3 Bg7, 7.Ng5 d5, 8.f4, again with more space for white.
If black plays Aljechin he must not be afraid of lack of space.
Here's an illustration of the intended outcome after Bc4 that TonightOnly pointed out. I'm not sure that white is terribly disadvantaged here. Black will have to move his king immediately to take him out of harms way, and then white can develop the king's knight getting ready for castle.
Yes, which is why chessgames.com shows ...e5 as the FAR more common move than taking the e pawn. However, we've come to the conclusion that Nxe4 eventually leads to an awkward position for white. Why would black not what this? What is better about transposing to the bishop's game?
I have been recently experimenting with whites responses to black's Alekhine's Defence other than 2. e5. Chessgames.com shows Bc4 played 10 times with white winning 40% of the time. I thought I'd give it a shot, and innitially it looked brilliant. This is what I saw (starts to get interesting after these two diagrams):
Of course black should not move his king to escape check. Instead, black should protect with the knight. Like this:
This move sequence for black which is started with Nxe4 seems obvious - HOWEVER - Chessgames.com shows 2...Nxe4 played only 5 times and 2...e5 played 1,493 times! My question is - What he heck is wrong with 2...Nxe4? At the very least black is up a pawn and will have to retreat - possibly giving up some position. What makes 2...Nxe4 so deplorable for black as to be overlooked 1,493 to 5?
Here's the game chessgames.com shows: