I don’t have my Moodle configured for any kinds of learning objectives, so I am a bit in the dark about what Moodle maintains, what you are trying to do, if you are using a plugin, etc.
However, I do work for an AACSB accredited school, so I am a little familiar with what you desire.
In my own case, I have put one of my courses through a Quality Matters online-course audit. One thing that Quality Matters requires is a Course Map (here is my example.) This course map provides Course Objectives, Module Objectives, and connects these to specific activities. When I was working on my QM audit, I had to describe this connection between course goals, module goals, and assignments in detail. I even showed that every question I used in a quiz had AACSB objective (via the textbook’s question bank.)
I haven’t had to provide any of my work to my school’s AACSB accreditation process, but I have always thought that what I did for Quality Matters would certainly meet AACSB needs.
So it seems to me that a course needs to be designed, upfront, with valid objectives, and objectives that can be tracked. This is why I am not sure what Moodle might report. If AACSB were to question if my students satisfied the course objectives, I would show grade book results.
The real problem seems to be that few instructors and few administrators want to invest themselves in creating course maps, doing course comparisons, validating instruction, etc. So they look for easy solutions, such as "Can our LMS do this?"
Well, just some of my thoughts. I would appreciate more discussion from you or others.
Incidentally, I did give a presentation about my Quality Matters certification last year at MountainMoot. Here is some reference materials about it.
MoutainMoot2020 "Quality Matters Certification using Moodle"