I fully understand what your saying, but disagree profoundly that the TA has not carried out a service for you, and deserves paid for it. They are now providing more resource to chase your refund and that also costs money, unless you do it yourself by purchasing direct. Only you know your reason for using a TA, but is sounds like pounds, dollars, euros or whatever might have been part of it, and rather than admit your choice has got you to where you are, you're striking out at the TA as if they were in control of any cancellation.

Your choice of words ". . .the validity of the service is determined in whether the booking delivered by the agent can be consumed on the date of service" helps your case if it was true, but it's not. Making the booking as per your instruction was a line item as it were and was completed to both of yours' satisfaction. Dealing with subsequent issues is another line item, not usually required, and the two can not be combined just to suit your case.

I don't know where you've made the purchase so don't know the legal situation, but morally the Travel Agent deserves payment. None of us work for free so there is no doubt about that.

For openness, I have never worked in the travel business so have no personal axe to grind in this matter.