A Weapons Systems Officer (WSO) is a task/mission specific position.
When I was on the F-111, all WSOs are pilots and all F-111 pilots can be WSOs when needed. On the other hand, the F-14's WSO position is a non-pilot or non-aviator position. The F-14's WSO is called a 'naval flight officer'. On the F-111, if the pilot -- left seater -- is unable to fly the jet, the WSO -- right seater -- can take over as there is a control stick on the right side of the capsule. But on the F-14, if the pilot -- front seater -- is unable to fly, it is ejection time for both front and rear seats.
Both the F-111 and F-14 have unique cockpit controls for specific positions. For the pilots on the F-111 and F-14, instruments and controls are primarily for flight related issues. For the WSOs, instruments and controls are primarily for mission related issues.
The F-16I was designed with the same philosophy. While each cockpit can fly the jet, each cockpit have its own unique instruments and controls designed to separate tasks. The front cockpit is for flying, the rear cockpit is for whatever the mission is supposed to be.
Same for the F-15E Strike Eagle.
The reason the WSO is needed, whether the position requires a rated/certified aviator or not, is when the aircraft's missions (plural) increases to the point where division of responsibilities becomes necessary.
Task saturation...
https://www.nbaa.org/ops/safety/20130617-task-saturation-how-much-is-too-much.php
All jets can be flown with only the pilots but combat effectiveness will be drastically reduced without the WSOs.