While adding multiple layers at once to a new, empty map may not be a common practice, it does beg the question about how ArcMap chooses the default coordinate system when the coordinate systems of individual layers differ.
If you are adding all three geometry types at once (points, lines, and polygons), ArcMap will automatically set the drawing order so that polygons are on the bottom, lines are in the middle, and points are one top. If you are adding more than one layer of the same geometry type at once (i.e. two point layers), the drawing order within each geometry type is alphabetized in ascending order (A on top, Z on the bottom). This same logic is used when determining the default coordinate system, whereby the lowest layer (first one drawn) is used to set the default coordinate system.
For example, if you add a polygon layer with a Geographic Coordinate System (GCS) and a line and point layer, both with a Projected Coordinate System (PCS), the default will be set to match the polygon's GCS. Similarly, if you add a polygon layer with a GCS whose file name begins with an "A" and another polygon layer with a PCS whose file name begins with a "Z", the default will be set to match the "Z" polygon's PCS, because that is the lowest layer (first one drawn) in the map.
The same applies when adding just two geometry types (points and lines, points and polygons, or lines and polygons) or one geometry type only: the lowest layer in the drawing order—which is determined first by geometry type and then by ascending alphabetical order within each geometry type when adding more than one layer of the same geometry type—is used as the default coordinate system in ArcMap. Again, all of this applies to adding multiple layers at once. Otherwise, the default coordinate system is simply set by the first layer added to the map, unless it is set manually before any layers are added.
If you are adding all three geometry types at once (points, lines, and polygons), ArcMap will automatically set the drawing order so that polygons are on the bottom, lines are in the middle, and points are one top. If you are adding more than one layer of the same geometry type at once (i.e. two point layers), the drawing order within each geometry type is alphabetized in ascending order (A on top, Z on the bottom). This same logic is used when determining the default coordinate system, whereby the lowest layer (first one drawn) is used to set the default coordinate system.
For example, if you add a polygon layer with a Geographic Coordinate System (GCS) and a line and point layer, both with a Projected Coordinate System (PCS), the default will be set to match the polygon's GCS. Similarly, if you add a polygon layer with a GCS whose file name begins with an "A" and another polygon layer with a PCS whose file name begins with a "Z", the default will be set to match the "Z" polygon's PCS, because that is the lowest layer (first one drawn) in the map.
The same applies when adding just two geometry types (points and lines, points and polygons, or lines and polygons) or one geometry type only: the lowest layer in the drawing order—which is determined first by geometry type and then by ascending alphabetical order within each geometry type when adding more than one layer of the same geometry type—is used as the default coordinate system in ArcMap. Again, all of this applies to adding multiple layers at once. Otherwise, the default coordinate system is simply set by the first layer added to the map, unless it is set manually before any layers are added.