I fully agree with you re. 'shake your hand' but I have to defend the line manager at large companies: too often, they have their hands tied with yearly performance evaluation processes and bonuses and will likely be unable to fetch the employee the necessary raise outside of working within aforesaid processes (i.e. getting the employee a promotion in a higher pay band, etc.), which takes time. I say this not to defend anyone but to try to present a more balanced picture.

In a smaller company, I would be worried about 'revealing my hand' to a potentially vengeful manager asking for a raise and I would rather just leave than try to get them to counter offer. That is, if I ask for a raise and s/he denies it, I would feel that I would probably be the first one to get cut when the time comes so I might as well leave. In a larger company, I might try to work with the manager on a 'career plan' assuming the manager in question is not toxic; the toxic ones will pretty much ensure that one gets a 'needs-improvement' type rating, which pretty much limits any movement for the unfortunate employee from that point on.