I see your point, but I don't know...
It was nice when my wife was rushed to the hospital in the middle of the night, the entire elder body and their wives came up with our family to check on us. It was really nice and something I was appreciative at the time. That was when I was fully "in" and really thought they were shepherds for Christ. We tried not to impose on them or keep them up there too long. But it made a dire situation seem much better somehow.
I remember one time when I was younger, an elder who I confided in told me that I can call him whenever I needed, even if it was in the middle of the night. He said if I was afraid to call him or "bug" him, then he wasn't doing his job. He also said that if there was ever a day when he's "too busy" for me or anyone in the congregation, then he doesn't qualify to be an elder anymore.
It really adjusted my perspective some.
But on the flip side of that, I've known and seen many examples of ones who constantly and relentlessly call the elders, bugging them for the most asenine and trivial matters. They treat the elders like door mats and act as if the elders should cater to their every whim in order to "shepherd" them. That I can understand. That is NOT okay. No wonder half of the elders are worn out!