Relevance: from the cited paper, the variance of the median estimator is proportional to 1/(n * f^2), where n is the sample size and f is the density at median.
Two observations:
1. With sufficiently large n, you can control your variance to an acceptable level.
2. The factor f is outside of your control. If your problem has a small density around the median, then you'll need to throw more samples to compensate for it.
I think your concern is about #2: you can always construct a pathological distribution to make the sampling-based approach unattainable. The paper provided guidance on what to expect when you apply the sampling-based approach.
Two observations: 1. With sufficiently large n, you can control your variance to an acceptable level. 2. The factor f is outside of your control. If your problem has a small density around the median, then you'll need to throw more samples to compensate for it.
I think your concern is about #2: you can always construct a pathological distribution to make the sampling-based approach unattainable. The paper provided guidance on what to expect when you apply the sampling-based approach.