That's why I think we should only perform reachability checks when we already know or at least have a strong suspicion that something is wrong.
One possible exception is session establishment: it might be useful to try several setup attempts in parallel, as the one that completes the fastest is probably also the one that offers best peformance during the session.
Don't this open up for a new DDoS? Interrupt the transport on both sides, or at a (or multiple) site exit router, enough to cause a storm of setup attempts?