Note that I'm not implying these figures are true of either HAProxy or nginx, just pointing out that the OP is probably correct that the number one feature of a load balancer is its ability to load balance. Good monitoring makes it easier to use, though.
The truth is that most load balancing solutions are capable of handling _a lot_ of traffic, way way more than the majority of the people need. So performance is not a huge concern, typically.
However, if you are at the level where it does actually matter and want to use nginx, chances are, you'll have no problem paying for the premium version.
HAProxy has a status page to see how many requests are processed and going where. nginx doesn't.
Monitoring is essential to any infrastructure, regardless of its scale.
This is a bad analogy, because 'flying blind' in a plane means you can't use it effectively. Being able to see out of a plane isn't a 'bonus'; it can't be used without this feature. Whereas plenty of people can and do use a load-balancer without heavy monitoring. (not to mention that there are strong moves towards self-driving transportation at the moment)
The analogy also doesn't work because a loadbalancer that can handle 1000 units is going to have far fewer problems that are in need of diagnosis than one whose limit is 100 units; when the traffic level is between 100 and 1000. When the traffic is at 100, then yes, you're going to want monitoring on the 100-unit LB, because you're trying to squeeze extra performance out of it. Whereas the 1000-unit one isn't even sweating at that point.