In theory your right, the hairdresser should try harder to try and retain your custom. However in reality this will not be the case. The salon will either put you in with a inexperienced stylist or the stylist will be annoyed that thye have to do a free cut and may rush so they can fit in a client after. Most stylist in medium to high end salons are on commission, have average bill target and retail goals. They may see this free hair cut has having a bad effect on there results.
You just need to ask yourself would a good stylist or salon really need to give away free haircuts? i know we would never do it in our salon, even if your not busy your would be better off offering reduced price cuts to exisiting customer and not support a multi-million pound company like herbal essence by doing things for free.
By all means go - its free at the end of the day, just don't expect miracle and do expect them to try and sell you products. but if you brought shampoo before why would you.
Just my opinion for experience from the hairdressers salon point of view.