ImageMosaic can support mosaics of data with different CRSs. (Think about a collection of sentinel data with different UTM zones).
In ImageMosaic, a single common CRS is exposed as the native CRS of the whole collection (as an instance WGS84).
When dealing with an HeterogeneousCRS mosaic, all the read requests get internally reprojected to the common CRS.
So, a raster download with targetCRS = UTM 32N of a UTM 32N granule results into:
a read of that granule
an internal reprojection made by imageMosaic to common CRS (i.e. WGS84)
an additional reprojection of the reprojected coverage, back to Target CRS = UTM 32N
It would be great to recognize this situation and avoid the double reprojection