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Hopefull: So the agency has to eat the rest of the price.

I'm not aware of any agencies in this area that "eat the rest of the price". More commonly the individual pays all of the fee up front and then applies to be reimbursed through their insuring party up to the amount provided. For example, if the cost was $150.00 and the insurer only covers $80.00, the client will "eat the rest of the price".

Typically, insurance is offered as part of an employment benefit package but benefit packages are generally not offered for menial workers (i.e. waitstaff, janitorial, child care workers, etc.) No benefits package = no insurance. This means that those engaged in specific fields or those who are not employed at all can often not seek therapy for the simple reason that they can't afford it.