So other than the historical relevance (by which you mean mongol-turkics hundreds of years ago ruled parts of present day India) there is nothing that modern day Republic of Turkey has to offer in the Kashmir issue to the Republic of India, right? Thats precisely why we don't want you as mediators.
It's not just Turkey, it is the same with any other country - in the past we have also said "thanks, but no thanks" to American offers to mediate. We consider Kashmir as our integral part, and we don't want any mediation on it. And militarily we are confident that we can keep it, and prevent our neighbours from stealing it. We will keep doing these useless talks with Pakistan, because that keeps them under the delusion that they are doing something. At the end of the day, we are not going to give up an inch of territory to Pakistan, whether they talk their way into it, or try force as they have done and failed in the past.