ICAO homepage puts safety as the first objective:
No it doesn't. It says:
Safety is a core value-offering of rapid and dependable air services,
Note,
A core value, not
THE core value, which means there are other equally weighty or competing values.
ICAO says their core is:
Its core function is to maintain an administrative and expert bureaucracy (the ICAO Secretariat) supporting these diplomatic interactions, and to research new air transport policy and standardization innovations as directed and endorsed by governments through the ICAO Assembly, or by the ICAO Council which the assembly elects.
Bureaucracy is their core function. That's why they only have "Strategic Objectives" rather than actually do anything.