Why did this old Japan Nakajima J1N airplane use a Yagi rather than a parabolic antenna?
Note that the assertion "It can only receive signal if the transmitting antenna is not exactly in front of it" is wrong. The most sensitive direction for receiving is in fact exactly in front of the antenna, so if the incoming beam is directly in line with the yagi shafts, the maximum signal strength will be received.

A parabolic antenna would be bigger across than the width of the plane's fuselage, causing a huge amount of (unnecessary) drag.