Anycast is certainly a nice layer to add but it's not a requirement for DNS round robin to work reliably. It does save some of the concern around relying on selection of an efficiently close choice by the client though and can be a good option for failover.
More directly - is there some set of common web client I've been missing for many years that just doesn't follow DNS TTLs or try alternate records? I think the article gets it right with the wish list at the end containing a Amazon Route 53-like "pull dead entries automatically" note but maybe I'm missing something else? I've used this approach (pull the dead server entries from DNS, wait for TTL) and never caught any unexpected failures during outages but maybe I haven't been looking in the right places?
If you mean it's possible to design something with round-robin DNS in a way that more clients than you expect will fail then absolutely, you can do things the wrong way with most any solution. Sometimes you can be fine with a subset of clients not always working during an outage or you can be fine with a solution which provides slower failover than an active load balancer. What I'm trying to find is why round-robin DNS must always be the wrong answer in all design cases.
