I’m a big fan of cookie persistence. It solves so many problems, and it makes persistence nearly 100% effective in just about any situation. It’s also a lot easier to flip a switch to enable cookie persistence than it is to bypass an application platform’s native session handling. Why write your own stack on your own (or someone else’s application) in order to keep stateful information shared among servers, when you can just flip a switch? As preposterous as it sounds, I’ve heard that suggestion before.
Of course, it only works for HTTP traffic (and HTTPS if you terminate at the load balancer), but you typically only need persistence for HTTP traffic (SMTP doesn’t require it, for instance).

