It wasn't chosen at random. It swapped main FC's every boot, and each FC only took one AoA sensor as input. So if one fails, you'd only see it every other flight, and at that, only once you hit a flaps up configuration.

There was no automated cross-check out of the box.

Part of the reason for that setup was that Boeing knew if they implemented a multi-sensor solution, it'd require class D simulator training, which they were trying to avoid at all costs. See the 60 Minutes 737 MAX exposé. They apparently had a whistleblower willing to attest to it.