Presumably the shortage of labor was still real, and if they needed to hire people, but couldn't poach, then they hired them from the rest of the talent pool. If that's the case, then removing the "cold calls" from the talent search might have had the effect of actually driving up salaries for those not working at these companies, since potentially reduced the supply.
If that's the case, then it would not have saved money, rather, it would have had the effect of simply shifting the money from going to existing Google/Apple/etc employees to applicants from smaller firms.
That is, it changed the distribution of spending, and probably in a more egalitarian way, distributing the spending over a larger pool, instead of simply fighting over, and raising the wages, of the small group of superstars at the big companies.
These companies are spending on R&D and increasing the percentage year over year, they are also spending huge sums of acqui-hires, and hiring faster than the local communities, or their own office space, can handle.
You could argue that excessive salaries are actually bad for allocation. Wall Street has infamously brained drained tons of the best and brightest to figure out how to gain small efficiencies in stock trading. What discoveries might have occurred had string theorists not left to go optimize portfolios?
One thing I wouldn't call engineers is cheap. You're talking about people making upwards of $150-200k in salary, and probably up to half-million when total compensation is considered. I paid more in taxes last year than my mother earned in several years of working as a cashier. And that's pretty sad. I grew up poor so I have a different perspective on this, but I see a lot of #zeroethWorldProblems whining going on in the valley while the world around them is falling apart. It's useful to have some perspective, and honestly, if these companies are to be fined and sanctioned, I'd rather the money go to poor people, instead of lawyers and techies who need to increase the bid on their studio apartment.