I'm not familiar with the United system, but the Delta system is great.
The screens display full standby list, live and constantly changing as new people check-in. If you are flying a peak hour flight to Atlanta and trying to standby on an earlier flight, seeing that you are number fifty-five on a plane with only 3 unsold seats and only 8 non-check-in seats means that you can leave the crowded gate area and grab a bite, etc., without the stress of waiting for the gate agents to yell out those who cleared.
Most importantly, it clears up work for the gate agents so they actually have more time to get the flight out on time, while processing more upgrades!
1. Passengers are no longer asking the gate agents where they stand on the waitlist, so the gate agents can just deal with passengers checking-in, etc.
2. When it comes time to clear the upgrades (or Coach Class standby list), all those who clear transfer to a new screen on the flatscreen displays with their new seat number. They can take their old boarding pass to the boarding door, and the electronic gate reader will spit out a new receipt for the new seat. If you are upgrading, it will deduct the e-upgrade points. While many gate agents do the traditional blurt out the names and issue BP's at the gate, they don't have to. So more pax get upgraded with less work for the gate agents!
That's how it works at Delta. I'm not sure if United EasyCheckIn is that advanced.