It becomes apparent that our clients need our services when they start suggesting things that don’t make any sense and we have to explain to them why it’s a bad idea.

sometimes you just have to let the client try their bad idea and make mistakes because they’re ultimately the ones paying.

They are there to give credence to the manager's ideas ("Look, we've just spent $50,000 to have [consultancy] review this idea and these are their results!")

If the suggestions are good,

If the suggestions are crap

we are supposed to be curious

Asking "dumb questions", "failing fast", and leading with hypotheses are part of the consulting toolkit.

I'm no fan of any firm, but in their defense they might ask naive questions because it's not their field of expertise and because there are tons of easy improvements that companies just miss.

show why it was worth it and show what we contributed

These consultants are hired because they get to bypass the office politics that regular colleagues have to go through on a day-to-day basis.