But, in all fairness, even without the "AoA disagree" indicator there were telltale symptoms on the Lion Air bird that something was wrong with the alpha vane (the sensor in question). The most obvious was that only one stick shaker was going off (each control column has a shaker which only takes input from the alpha vane on its side). That's a pretty obvious symptom.
However on the previous Lion Air flight there were two other symptoms written up in the maintenance log[1]: "IAS (indicated air speed) + ALT disagree shown" and "(elevator) FEEL DIFF PRESS light illuminated". On the MAX, both of those systems take angle-of-attack into account (which is new for the MAX, IIRC).
As an aside, American Airlines 191 had a similar situation. Their DC-10 had only a stick shaker on the captain's control column, a second stick shaker was a paid extra. Boeing, of course, bought McDonnell Douglas years later.
1: http://www.jacdec.de/WP/wp-content/uploads/2018/10/2018-10-2...