You are supposed to take the promotion, update your linkedin, and find a real position with that title elsewhere for more money.
So those people aren't (usually) leaving to a competitor, but mostly to a current (or possibly future) client.
Same with law firms, auditing firms, etc.
> Hire young people for cheap and then let them move to future customers for high salaries.
Well, consulting salaries are usually significantly higher than industry salaries. So it is actually the opposite.
People move out of consulting because of the stressful hours and the up-or-out culture. Additionally, as you progress, the work goes from IC to project management then to client management (as a principal) then to sales when you become a partner. They tend to make less money when moving to industry (not always) and work fewer hours, and travel less too.
Bring people in on the cheap (partly because they're being paid in prestige), fly them around the country on miles you've prebought, work them really hard for a few years, and nurture them as they move on as future customers seems to be working out pretty well for them.