With a scheduled test, you have the benefit of having the main power actually working if the backup being tested comes crashing down; seems to me that mitigation would be much quicker in a scheduled test than in a real outage.
I suspect a monthly test - if communicated to customers as well - would drive better customer behaviour, e.g. multi-AZ usage, automated validation of EBS, adding extra machines in another AZ automatically. Maybe start with one or two AZ's with an opt-in from customers.
It's the same as advice to routinely replace your live data from backups. It's not a real backup until you've tested that you can recover from it.
It's an interesting and well studied area of statistics for medical tests.
eg. If you have a test that is 99% accurate and a treatment that harms 1% of the patients and you do this screening of a million people - how common does the disease have to be before you cure more people than you kill ?