We have a pool of elastic IPs that we rotate with Route53 using latency based routing. The ability to move the IP atomically (by moving the ENI) gives us operational flexibility. We were pretty surprised ourselves that the (huge) hotspots in our traffic distribution alone were enough to "break" the ELB, despite overall traffic being fairly low. We had to see it ourselves to believe it. The current setup has worked out well for us as we've scaled over the last year.

Also I'll add here to another point made below: I don't blame the ELB for not being built to handle our traffic pattern, despite the fact that websites are probably a minority on EC2 vs APIs and other servers. My specific critique is that none of their instrumentation of the performance of your load balancer indicates to you that there is any problem at all. That is... unfortunate.