Why isn’t there a DNS AA record?

This would be A Alternative – and would allow DNS-level failover.

There are MX records with priorities, so SMTP hosts can have multiple records, why not standard A records?

Web browsers, proxies even ftp clients & RSS readers could be configured such that if the first AA lookup fails, the next highest priority is checked (and of course if priorities are even, one is chosen at random), eg:

webscalability.com    AA 20  165.43.22.9
webscalability.com    AA 5   209.22.9.88

This idea could even be taken further with geolocation information.