The don’t reapply language is inserted to prevent further discrimination suits. It evolved from famous cases where the company settled with someone claiming racial or sexual discrimination, they clearly did not want that person around, but then did not hire him or her when they applied for there old job, one where they were clearly the most qualified.

jjv

Except as provided in this chapter, every contract by which
anyone is restrained from engaging in a lawful profession, trade, or
business of any kind is to that extent void.

The chapter goes on to provide a few discrete exceptions for sale of a business (B&P Sec. 16601), withdrawal or dissolution of a partnership or LLC (B&P Secs. 16602, 16602.5) and customer lists of answering services and employment agencies (B&P Secs. 16606, 16607), but nothing remotely analogous to an associate’s position at a law firm. Independent consideration is irrelevant. [Whether the provision in question should be considered a non-compete is, of course, a wholly separate issue. To the extent it only prohibits her from seeking employment from PH itself, and not from any "Released Parties" who may leave and start firms of their own, it's probably not.]

As to mandatory arbitration clauses, I don’t think Armendariz can be reasonably read to prohibit mandatory arbitration agreement generally. Quite the contrary, it gives a pretty clear blessing to any mandatory arbitration agreement that (1) provides for neutral arbitrators, (2) provides for more than minimal discovery, (3) requires a written award sufficient to ensure that the arbitrators complied with the law, (4) provides for all relief that would otherwise be available in court, (5) does not require employees to pay unreasonable costs or fees peculiar to arbitration and (6) is not otherwise unconscionable (e.g., doesn’t require one party to arbitrate while leaving the other free to litigate). I’d be very surprised if Paul, Hastings has a mandatory arbitration clause for its California employees that does not comply with Armendariz.

In this case, PH is providing independent consideration. Stilll, the California courts are remarkably hostile to these agreements for employees, and would tend to construe it against PH at every opportunity. (Surprisingly sensibly, these types of agreements are consistently upheld in sales of businesses, professional practices, etc. as not doing so would impair the market.)

The more important element here for PH is the release of claims, rather than the non-compete. Clearly this woman is primed to sue. Another quirk of California law is that binding arbitration clauses in employment agreements are extremely disfavored and are frequently found to be unconscionable.

Elsewhere people have suggested that the reason for forbidding applying for work is to remove any doubt that there was a promise of re-employment, and to avoid future employment actions based on the status of the person as a protected class with respect to employment discrimination. That is, even though pre-existing claims were waived, the person could theoretically generate a new claim by re-applying and being turned down.