you don't need to burn the burner phone necessarily. Just take out the battery and store it somewhere safe.
Maybe I expressed that a bit unclear: I didn't mean it fails because you have no longer access to the number (= you burned the burner). It fails because Twitter don't accept this same number which worked while sign-up anymore for re-verfification.
To be honest: I'm not sure if Twitter accepts any other number in that case or if the prompt for phone number re-verification is just an obscure way of saying "Your account is permanently locked for any reason."