Why can an elliptic curve private key be 1?
By the same argument, they would have to forbid $d = 1234$; after all, an attacker can trivially compute the value of $1234 G$; and if they see it, then they can immediately infer $d$ without having to complete a discrete log over an elliptic curve.  Of course, this logic would forbid all possible values of $d$...

The issue is that if the attacker gets lucky and guesses $d$, he wins (and there's nothing special about $d=1$ in this).  However, he is quite unlikely to get lucky (and again, there's nothing special about $d=1$ in this either).