This model can potentially be flipped, with the recruitment consultant being paid from, and in proportion to, the increase in salary of the employee they place in a new job. The recruitment consultant would operate on a "no pay-rise, no fee" basis. This way the employee always wins (assuming they pass the interviews), as the fees would be less than the increase in income.
An interesting aspect of this model is that the recruitment consultants would be most incentivised to place employees that are underpaid relative to their market rates - the more they are under-paid, the more the recruitment consultants can make. This could potentially have a levelling effect on the market.