Global load balancing: GeoDNS vs Anycast vs application-level routing

we're expanding our infrastructure into asia and europe, and global load balancing is becoming a big deal. right now, we're mostly using geodns, but we've run into issues with dns caching by ISPs causing requests to hit sub-optimal regions, sometimes for minutes. anycast seems like a good solution for latency, but the BGP expertise needed on our ops team is a high bar, and troubleshooting can be a nightmare. then there's application-level routing, where we'd have a global load balancer that then routes to regional clusters. this adds another hop and complexity in the application layer, but gives us a lot of control. what are people's experiences with these? especially around failover strategies for each. if an entire region goes down, how quickly do users get routed to the next best region with each approach, and what's the blast radius like?