Why do you need a low ttl for those? You can add multiple IPs to your A/AAAA records for very basic load balancing. And DNS is a pretty bad idea for any kind of failover. You can set a very low ttl, but providers might simply enforce a larger one.
And then if you're dealing with browsers, they're not the best at trying everything, or they may wait a long time before trying another host if the first is non-responsive. For browsers and rotations that really do change, I like a 60 second TTL. If it's pretty stable most of the time, 15 minutes most of the time, and crank it down before intentional changes.
If you've got a smart client that will get all the answers, and reasonably try them, then 5-60 minutes seems reasonable, depending on how often you make big changes.
All that said, some caches will keep your records basically forever, and there's not much you can do about that. Just gotta live with it.
And a BGP failure is a good example too. It doesn't matter how resilient the failover mechanisms for one IP are if the routing tables are wrong.
Agreed about some providers enforcing a larger one, though. DNS propagation is wildly inconsistent.