Why does Smart's attack only work on anomalous curves?
You can find an answer at section 5.4 of Washington's Elliptic Curves: Number Theory and Cryptography. 

Following their notation (and skipping the technical details about reduction $\mod p$ and $E_r$ subgroups), let $N=\#E$ and assume $p\nmid N$. Let $\ell_1=\lambda_1(N\tilde P)$, $\ell_2=\lambda_1(N\tilde Q)$, so that $k\equiv \ell_2/\ell_1 \mod p$ (we want to prove this). Set also $\tilde K = k\tilde P-\tilde Q$. We have

$$k\ell_1 - \ell_2=\lambda_1(kN\tilde P-N\tilde Q)=\lambda_1(N\tilde K)\equiv N\lambda_1(\tilde K) \mod p.$$

In the last step you cannot continue, because the initial assumption makes $N$ invertible $\mod p$ and you can't say that this equals $0$, failing to prove that $k\equiv \ell_2/\ell_1 \mod p$. You can see that this proof does work if $p$ divides $N$. 

To my understanding, this would mean that if $p$ divides the number of points, then you may also perform the attack, but I haven't read enough on it to confirm this.