They do - by my observation, 19 out of every 20 people who have been in a position to evaluate the work of H-1Bs report that they are script-driven drones. In theory we could simply let the next-quarterly-report driven corporations reap the eventual consequences of valuing cheap over truly qualified - the problem is that they'll gut the American middle class in the meantime.
That is a problem which is not unique to H1B visa holders. It is a problem with Boards of Directors, get rich quick players in the stock market and prestigious schools of management.
There is a converse to your truthful statement: Corporations believing high-priced senior management is always better.
A Brigadier General (One Star) has a maximum monthly base salary of $12,471.09
A full General (Four Star) has a maximum monthly base salary of $19,960.59
The abilities required to "manage" a Division or an Air Wing are different but in many ways more complex than those needed to run a corporation. The "CEOs" in the military are not exactly rolling in the big bucks.