Proponents of deploying LTE in the 5 GHz band for providing additional cellular network capacity have claimed that LTE would be a better neighbour to Wi-Fi in the unlicensed band, than Wi-Fi is to itself. On the other side of the debate, the Wi-Fi community has objected that LTE would be highly detrimental to Wi-Fi network performance. However, there is a lack of transparent and systematic engineering evidence supporting the contradicting claims of the two camps, which is essential for ascertaining whether regulatory intervention is in fact required to protect the Wi-Fi incumbent from the new LTE entrant. To this end, we present a comprehensive coexistence study of Wi-Fi and LTE-in-unlicensed, surveying a large parameter space of coexistence mechanisms and a range of representative network densities and deployment scenarios. Our results show that, typically, harmonious coexistence between Wi-Fi and LTE is ensured by the large number of 5 GHz channels. For the worst-case scenario of forced co-channel operation, LTE is sometimes a better neighbour to Wi-Fi - when effective node density is low - but sometimes worse - when density is high. We find that distributed interference coordination is only necessary to prevent a "tragedy of the commons" in regimes where interference is very likely. We also show that in practice it does not make a difference to the incumbent what kind of coexistence mechanism is added to LTE-in-unlicensed, as long as one is in place. We therefore conclude that LTE is neither friend nor foe to Wi-Fi in the unlicensed bands in general. We submit that the systematic engineering analysis exemplified by our case study is a best-practice approach for supporting evidence-based rulemaking by the regulator.