IME you end up with both; something like discrete client, LB, and controller. You can’t rely on any one component to “turn itself off.“ ex a client or LB can easily get into a “wedged” state where it’s unable to take itself out of consideration for traffic. For example, I’ve had silly incidents based on bgp routes staying up, memory errors/pressure preventing new health check results from being parsed, the file systems is going read only, SKB pressure interfering with pipes, and of course, the classic difference between a dedicated health check in point versus actual traffic. All those examples it prevents the client or LB from removing itself from the traffic path.
An external controller is able to safely remove traffic from one of the other failed components. In addition the client can still do local traffic analysis, or use in band signaling, to identify anomalous end points and remove itself or them from the traffic path.
Good active probes are actually a pretty meaningful traffic load. It was a HUGE problem for flat virtual network models like a heroku a decade ago. This is exacerbated when you have more clients and more in points.
As a reference, this distributed model it is what AWS moved to 15 years ago. And if you look at any of the high throughput clouds services or CDNs they’ll have a similar model.