Trimming the fat, wouldn't it be more effective to trim from the top where the big paychecks are?

Does it make sense to cut the fat from the very people needed to operate the company/business? You hear news sources, the paper and magazines saying this company or that business is cutting jobs to save money. If you need workers on the line to build or make the widget why trim them off? How often do the middle and the top get trimmed? If you don’t have a product because you have no one to make it what is the middle and upper managers and execs suppose to do, compare golf scores or who bought the biggest boat? Like having a team with many, many coaches and no players, why would they be needed? Shouldn’t the biggest trimming of fat comes from stream lining the top where the biggest paychecks are instead of trying to equal those cut by slamming most of the bottom?