Analysing hydrologically corrected DEM avails an opportunity to calculate morphometric indices such as drainage basin density(DD) (which takes manual approach). Can not DD and others be extracted automatically?
You might check out a few papers in my Researchgate, such as Stream Types and Management Implecations, and a couple involving LiDAR. DEMs created from normal topographic maps at 1:125k and 1:24k are helpful, but the DEMs from the LiDAR is much more detailed, and the channel network expands on average about two orders. The LiDAR pulses can see through vegetation layers, but are absorbed by water. Basically with the DEM from LiDAR, one can properly obtain high quality georeferenced stream and channel network, and many other ground features as old roads, drainage ditches, wetland depressions, archeology or construction sites, realigned or diverted streams, beaver dams sometimes, etc. There are some hydrology tools in ArcMap, and I had GIS and LiDAR expert help, but from work from the 1980s to work that extended to about 2015, the tools needed careful review and many edits to create final products. The hydro tool in ArcMap identifies what it determines to be the main or single thread channel, so the complexity of split or braided channels are not identified without added editing. Channel barriers as road crossings need to be removed, and there may be instances where the channel is diverted onto the floodplain, and cannot find its way back to its channel without editing. I think there may be a stream ordering tool in ArcMap, but again, I would expect final results to take substantial editing. You can expect the normal topographic maps to have mistakes in georeferencing especially in heavily forested areas, some imperfect areas where channels join, especially for channels that cross floodplains or relatively flat terrain. In most places, relying on the blue line streams for the flow permanence network is insufficient.