It's an important metric for evaluating research production. Of course no metric is perfect, blabla. But it is a decent one. Despite the people who hate this, it is normal to see h-indices listed (even as a field) in nominations for rewards for instance. And hiring and compensation committees look at it.
Again, it's not perfect (can be gamed, other metrics may show things it doesn't). But it is a very simple reasonable first cut. But I think talking to scholars in the field is actually the superior metric. People know who the big/medium/small wheels are. And which are tires that fell off the car and are sitting on the side of the highway.
Finally while being with a big name is ceteris paribus, a very reasonable variable to raise, it is not the only one in looking at advisors. I.e. research production =/= good advisor. You need to consider other things like is the fellow a jerk or nice, how fast do people graduate, is it a huge lab group or tiny, current funding, etc.
For instance, I would be inclined to avoid professors working on tenure (they may not get it, or may need to be slave drivers to get it) and would prefer someone who was a big wheel but is winding down (maybe 60 or so in age). Even the jerk, slavedriver big wheels tend to get a little more kind and grandfatherly towards the end. And reputation has a long dwell time, so it's not as critical for an old, established scientist if he goes emeritus shortly after you worked with him (might even be an opportunity for you to sneak under the wire).