It would be great if Mosaic To New Raster could support snap raster. This would ensure the "snap" of the output raster without unnecessary resampling later.
As far as I know, Mosaic To New Raster has never supported snap raster.
I suspect there may be a reason snap-raster may cause some issues in some workflows. If so, maybe that particular workflow that is preventing use of snap raster could be tagged with a warning or error before the tool runs if a snap raster is set? It sure would be nice to have it available.
This would remove a reason I miss the Merge tool
Bring back Spatial Analyst Merge tool