Usually it’s not the consultants, but the clients who drive these outcomes. I think like OP consultants would happily deliver answers, explore unknowns, create tools, and lay business roadmaps. There must have been something attractive about BCG work besides the name and the pay - that ideal, working on diverse projects and affecting change and improvement isn’t impossible. But as was said, you’re usually hired to give a predetermined answer rather than actually solve a problem.
The problem is that when you interview for BCG evrything is about how you can solve problems. I understand the frustration when you are young and idealist and discover that was a lie for 50% of your projects.
That's actually a separate area of practice: "Human Capital Consulting". In addition to laying off people, they also do systems integration for stuff like payroll.
Sounds kind of like the person who goes to a therapist because their spouse told them "you need therapy..." Don't expect anything meaningful to come out of the exercise.