Or is this the intended behavior of QGIS upon export to GeoJSON and I'm thinking about this wrong?
I don't know what the intended behaviour of QGIS is, but if the intention is to write GeoJSON according its specification (https://tools.ietf.org/html/rfc7946) or just RFC7946 for short. Then yes.
Section 4 of RFC7946 tells us that
The coordinate ...
I think that this is not possible (though Andrea may correct me) -
Consider the following program:
CoordinateReferenceSystem src = CRS.decode("EPSG:32066");
CoordinateReferenceSystem dest = CRS.decode("EPSG:4326");
MathTransform transform = CRS.findMathTransform(src, dest, false);