They do exactly that already.
Credit Request and Payment Procedures
To receive a Service Credit, you must submit a claim by opening a case in the AWS Support Center. To be eligible, the credit request must be received by us by the end of the second billing cycle after which the incident occurred and must include:
1. the words “SLA Credit Request” in the subject line;
2. the dates, times, and affected AWS region of each Unavailability incident that you are claiming;
3. the resource IDs for the affected Included Service ; and
4. your request logs that document the errors and corroborate your claimed outage (any confidential or sensitive information in these logs should be removed or replaced with asterisks).
If the Monthly Uptime Percentage of such request is confirmed by us and is less than the Service Commitment, then we will issue the Service Credit to you within one billing cycle following the month in which your request is confirmed by us. Your failure to provide the request and other information as required above will disqualify you from receiving a Service Credit.
There's most likely a reason for this.
Like, maybe in the past AWS customers have tried claiming for SLA credits for incidents that didn't impact them, in order to reduce their bill.
The mechanism can be really simple. If AWS themselves posts an outage to their status page and/or some third-party service posts an outage then credits are immediately applied to the services where there are outages for those that paid for high level uptime guarantees without requiring any claims process. It can easily be done if they want to do it that way.
Of course from a business perspective I understand why they're doing it the way that they are. If they can make customers jump through hoops, then only those who really care will follow through. Meanwhile the uptime guarantee can continue as an empty promise.
Also: requiring your customers to ask for their money back when you know that you didn't deliver the service promised and all other billing is automated.. come on.