Re: You're safer with paper.
Ground movement control systems are not commissioned overnight. National regulators require a safety case in which all possible aspects of a system's operation are considered, including operating procedures, environment, traffic patterns, human interaction and failure modes. The system only goes into operational use if the remaining risk is acceptable to the regulator. Back in 1998 the Internationbal Civil Aviation Authority (ICAO) deemed A-SMGCS just as good as looking at traffic out the window, that is the level of sophistications these systems attained already back then.
A typical required reliability figure would be 99.995% uptime. To properly monitor all ground traffic, aircraft and vehicles, there is often multiple coverage by radar, multilateration and ADS-B (Automatic Dependent Surveillance - Broadcast).
The systems are designed for high availability with redundant hardware spread over at least two locations and duplicated data links with physically separate pathways. The design allows for graceful degradation so that if central processing fails, the radar image is still available.
Runway access is controlled by stop bars, often with microwave barriers that will detect runway incursions. If a stop bar is off, that does not mean that a crossing is safe, but if it is on, the pilot knows it is not safe.
Moreover, Air Traffic Controllers are trained to deal with system failure. In that case, they switch to procedural air traffic control, doing everything in their heads with of course a much reduced traffic flow.