What is White's refutation to the Cordel gambit in the classical Ruy Lopez?

The position comes about after 1. e4 e5 2. Nf3 Nc6 3. Bb5 Bc5 4. c3 f5 (imgur.com/a/Lmdt6w5). It was played famously in the game Gufeld v Kavalek in the 1962 Student Olympiad. Of course, white plays d4 attacking the bishop, and black takes fxe4, but after that, it's such a mess of tactics for white, that I don't understand why it's out of style. Even if white has all the variations analyzed, he doesn't gain a winning edge, and black's game is very playable. Is there something I'm missing, as to why it's out of style?

I think it's because after 5. d4 fxe4 6. Bxc6 dxc6 7. Nxe5 black has to move his bishop back, and white has an obvious advantage because of the strong knight on e5, black's weakened kingside due to the absence of the f pawn, and white's superior pawn structure (black will probably have to focus on defending the isolated e4 pawn, especially since white can castle, play Re1 and Nd2 which both attack the pawn.)

Yes, see how Anand plays it: