Air traffic control systems should at least be 2oo3[1] (3 systems independently developed of which 2 must concur at any given time) so that a failure of one system would still allow the other two to continue operation without impacting availability of the aviation industry.
Human backup is not possible because of human resourcing and complexity. ATC systems would need to be available to provide separation under IFR[2] and CVFR[3] conditions.
[1] https://en.wikipedia.org/wiki/Triple_modular_redundancy
[2] https://en.wikipedia.org/wiki/Instrument_flight_rules#Separa...
[3] https://en.wikipedia.org/wiki/Visual_flight_rules#Controlled...