I suspect the concept of measurement invariance makes no sense for casual indicator models. The whole idea is that two people who have the same level of a factor should have the same expected response pattern. That only works if the items are reflective.

Hmmm, something about that still isn't clicking for me, because causal indicator (vs composites) still have measurement error + residual variance, allowing for the higher order construct to not perfectly match the data provided by the indicators, yes?