It's not always that leadership ignores line-engineers just because they consider them stupid. Even obvious recommendations get tangled into the web of politics and personal favors. Sometimes the 'obvious solution' is also a play to get more power or influence for someone you're opposed to. That factors into how the advice is taken.
Part of the fiction management sells itself is consultants can cut across those organizational boundaries and find the 'right solution'. Sometimes having an 'impartial' voice echoing what others have already said is enough to convince you it's not just someone trying to poach your turf, it's actually good advice.
Further, our tendencies towards tribalism influence this process. We tend not to think of other employees as part of the same group - they are devs, or ops, or product. That builds an 'us vs. them' mentality that's hard to break. Bringing in an outsider tends to unify the group into us (the company/team) vs. the outsider (the consultant). That psychology helps us to justify bitter medicine like our team getting more work (which will help the company).
I tend to have a negative opinion of consultants, but someone pointed this aspect of group psychology to me in the past and it resonated.