In the scenario of connecting as a station to a normal home-type wifi router, would having a high gain directional device like a LHG 2 improve the situation, or is it irrelevant as the home-type wifi router would need a similar antenna?
It may, or not, improve the connection. The higher gain antenna also have a better reception. So, the normal one would get a louder signal, and the higher gain would get a better reception of the normal one.
It MAY be enough to improve things - but it’s not certain.
You would generally get better receive rates at the client end but you may struggle in getting RX rates at the AP up. IT wouldn’t be uncommon to get a-symmetrical results. In PtP there would be little reason not to run matched antennas.
Equations for calculation of radio signal (path loss etc.) all take antennae gain into account. I’ve never seen equation that would consider Tx antenna gain differently than Rx antenna gain. Specially when considering only “useful” signal. Sometimes it is good to have lower gain antennae on one side and higher gain antennae on the other side to reduce interference on the first (low-gain) side … if using narrow-beam antennae doesn’t help (interference comming from almost exactly same direction as desired signal).
Which means that considering “good signal” antenna gain is antenna gain and it doesn’t matter if it’s on the “high-energy side of free space” (=Tx side) or on the other end.
In short: high gain antennae on one side of a PtP link only do not cause assymetricity of the same link.
It is slightly different in fiber optics where too high Tx signal can cause some weird non-linear effects inside fibre core resulting in bad signal propagation. Free space doesn’t exhibit non-linear effects when using “normal” Tx powers (high power can cause ionizing effects which mean degradation of signal transfer).