Nick's Law of Relative Bargaining Power: any exogenous change in relative bargaining power will cause some change in the market that restores the original level of relative bargaining power. If there is a taboo against employers quitting workers but no taboo against workers quitting employers, and if people fear breaking taboos, then something else will change that re-equilibrates the fear.I would say that one thing that might equilibrate the relationship is wages: in some sense, the lack of moral outrage at employees walking out on their employers should make it harder for employees to prove to employers that they are serious about not walking out on them as soon as they get a better offer. The result should be that wage contracts contain more elements to reassure employers of workers' sincerity, such as low entry wages and steeper wage schedules, or longer unpaid internships or trial periods before full-time work and benefits are offered, as well as rewards for investing in firm-specific rather than general (and portable) human capital. At the same time, the asymmetry in moral outrage should result in more unemployment for those who failed to overcome firms' apprehensiveness.
This reminds me of an interesting argument I once heard in the debate about outsized CEO salaries: making executives the target of public shaming and zealous scrutiny of their private lives should raise not lower CEO salaries, as CEOs will need to be compensated even more richly for working under such stressful conditions. That is, the public campaigning against outsized CEO salaries achieves the opposite of its stated goals.
A similar mechanism may be at work in this more general example: if we make it hard for firms to fire employees, they will be reluctant to hire them, and therefore protections for employees may paradoxically endanger their employment, even if the protection is of a "moral" and not a "legal" nature.