This is a problem at most major airports during the holiday system, and I'm pretty sure Delta recommends additional time during the holiday season; it might even come up with the check-in email. Regardless, they suggest a minimum of 2 hours for all US based itineraries. So you said you showed up 1hr 40 mins before and it was cutting it close, that's less than the recommended time. For your friend, not seeing what their confirmation said hard to say if 2 hours was sufficient.
Staffing isn't usually the problem in these situations. Like has been said, the airlines know they are going to be busy. The problem tends to be having enough counter space available to add additional agents and behind the scene throughput to process that volume of baggage. It does know good if I have a ton of agents standing up front but the bags are getting backed up because they're checked in faster than they can be processed. Ultimately the check in process is going to be constrained by the system the airport provides. For what it's worth, I flew out of MSP on 12/27 at 7am. It took 30 mins to get through the premium line, and who knows how long for the regular line. It happens, it's a busy time of the year, them having more staff wouldn't have been able to speed anything up.