The tread is thick, braced by steel belts and fairly rigid. The sidewall is thin and bends with every rotation while carrying the car's weight, so any plug or patch there is flexed constantly and the bond can fail without warning. That is why Michelin and TyreSafe both rule out sidewall repairs entirely.
The shoulder, where tread curves into sidewall, has the same problem plus higher heat. BS AU 159 limits repairs to the central three quarters of the tread width for that reason. If a nail has gone in close to the edge, a new tyre is the honest answer even when the hole looks tiny.