It is hard to say what is Bitcoin main purpose, especially since no one is in charge of deciding what it is. It is undefined. We can speculate about why it was created and what the creator Satoshi had in mind, but Bitcoin now belongs to the people and they can do with it as they please. A free transaction is obviously impossible and not intended as mining fees are planed to be the only way of miners getting payed when the block supply goes to zero in about 100 years.
It is hard to claim that it was mostly about lower transaction fees or anonymity, since the creation of Bitcoin happened right after the financial crisis and during the bank bailouts that decreased the value of fiat currency and effectively taxed the people for bank's mistakes and greed. The first Bitcoin block, the genesis block has references to the bank bailouts as it holds the headlines of British newspapers that read "Chancellor on brink of second bailout for banks" along with the name of newspaper and the date as to prove that block wasn't premined.