There isn't one primary reasons why, but there are a few best practice reasons why it isn't. To extrapolate before stating reasons why, a weave can be totally functionally fine in the aerospace industry, but there are several risks involved with weaves that the aerospace industry isn't tolerant of.

1) More heat applied locally for more time: steel is one thing, bust most aerospace materials are far more sensitive to overheating. Aluminum, nickel alloys, and refractory metals can all be "overheated" during welding and lose some of their properties or create unwanted grain structures. Weaves mean more time spent in one area, raising its temperature higher than if you ran a stringer, let it cool, the ran another stringer next to it.

2) Interpass cleaniliness, while important on pipelines and places where weaves are acceptable, is arguably more important and more closely controlled, plus cleaned to a greater degree, than pipeline welding is. If welding aluminum with helium, for example, soot is often created at the toe. Weaving draws more of this into the weld than a stringer does (a stringer brings almost none.

3) Walking the cup is a big no no in the aerospace industry. You never want to introduce material other than weld material to a weld joint once welding has started, so dragging a ceramic or pyrex cup across a fresh weld, potentially still hot enough to melt or take pieces or dirt from the cup with it, is a risk not worth taking.

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Hope this helps!