I'm guessing that it's because it takes a person to put snowfall data in (as well as measure it- hence why APA and others don't have any snowfall data), but the rest can be completely automated.
If true, that is ridiculous. Most PLCDs have contracted FAA observers recording snowfall and sent to NWS before CLIs are sent. Where is the snowfall measured "for" DEN? Of course it's no longer Stapleton, but if it's there on current DIA property, no reason why it can't be included in the reports. I may just pose the question on their facebook page.