I think the problems always arise when NNT and NNH are abused to infer efficacy of treatments. Afterall, statistics doesn't kill people, it's the practioners who do :).
See "Misleading Statistics" (2010, Hutton) (unfortunately, paywalled):
The major claim for NNT was that it is easy to understand, but this
claim has been refuted by observational and experimental studies.
An important problem with NNT relates to its supposed main advantage:
it is claimed that it provides a measure in terms of patients treated
rather than in terms of probabilities. However, this is not true. An
NNT gives the average number of patients, among whom, if they were
treated with one therapy rather than another, exactly one patient will
benefit. The NNT statistic is biased, and reliable confidence
intervals cannot be provided. Furthermore, there is no simple value
that indicates no difference between treatments. For meta-analysis,
NNT cannot be used directly because simple arithmetic, such as
addition, does not give correct results on the NNT scale. If the
baseline rate, e.g. the mortality rate on standard treatment, is
given, some transformations are required to be able to find the
mortality rate on a new treatment using the NNT. If the risk
reduction, the difference in rates, is given, the rate on new
treatment is found by subtraction.
From "The Numbers Needed to Treat and Harm (NNT, NNH) Statistics: What They Tell Us and What They Do Not" - Andrade, the whole section on Limitations of the NNT is particularly pertinent:
Consider a situation in which drug versus placebo response rates are
12% versus 1%, respectively; the advantage for the drug is 11%, and
the NNT is 9. Consider another situation in which the drug versus
placebo response rates are 99% versus 88%, respectively; the NNT is
again 9. These 2 situations are strikingly different. In the first
situation, there is almost no placebo response, and medication is
associated with a relatively large treatment gain. In the second
situation, there is a large placebo response, and medication is
associated with a relatively small treatment gain. Yet, the NNT is the
same in the 2 situations. So, it is really important for clinicians to
know not only what the unique contribution of the drug is (NNT) but
also what the placebo response and nonresponse rates are.