Depending on the level of the employee - it could harm them. For high caliber employees - you never apply - you get recruited. Do you think CEO positions ever make it to the online application list?
This is a true point and important distinction, but anti-head hunting agreements exist all the time, and aren't generally actively pursued by authorities. In fact, I don't even think 'no solicitation' agreements are illegal at all. Companies frequently spin this as part of agreements to a joint venture.
This was in a way a bit of a landmark case because the DOJ was actually investigating it for anti-competitive/anti-trust issues; ultimately, they settled though because while labor (an economic inputs good, by the way) was 'restricted', it wasn't a black and white violation of the Sherman Act as they weren't preventing employees from leaving or anything, just putting some select individuals on a 'do not call' list. I think in this case, it's pretty telling that all the DOJ did was settle the case and tell the companies not to do this again for five years.
What merited a response was probably that this included such a large group of high-profile companies that aren't even closely related (you can group them into three sub-groups by market), suggesting a large and collusive agreement that really can't be considered to be a joint effort or pro-competitive in any way.
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You've obviously never been recruited away by a competitor. When companies know that people are poaching their employees they pay better. If you as a company know you have nothing to worry about, you're less likely to give raises and large bonuses. Recruiters come with big raises for employees. It's not uncommon in my experience to see 30-50% raises being offered in tech. If Apple knew that wasn't going to happen they don't have to pay as well. That definitely hurts employees. It kills the free market.
In this particular scenario, it wasn't a company-wide no solicitation agreement, just that each company had a select "Do Not Call" list. In light of this, it's likely that only execs, top management, and key designers/engineers were on the list. So while I agree with your argument, I don't necessarily feel like this was something detrimental to employees as a whole, just a select few. Given this, I don't think the company's motivations are salary-related at all, as the types to be put on the no-poach list are paid very well already, but rather an issue of retaining key talent (and concerns about corporate espionage, re: AMD v Nvidia right now).
Also, in situations like this when you get recruited, usually you don't see huge raises immediately, but rather a very large bonus followed by conditional raises that can prove to be substantial if you earn them.