Taking something of an historical perspective to this, I believe it originates from the fact the Buddha and his Sangha refused any gratuity for their teachings as this may have jeopardized the integrity of the teachings. There were certainly sectarian contemporaries who were "in it for the money" and the Sangha wanted to avoid any such inference. In my mind then the focus should not be on the "Dhamma should be free" angle (which originates from god knows where), but rather "The Dhamma should not be exploited for personal gain
Often in these discussions, the subject of Dhamma books come up and whether they should be free. Often the subject of Bhikkhu Bodhi's valuable translations come into the discussion too. These translations are not free, but they are produced on a not for profit basis. If they were to be free to the end recipient, someone else indirectly would be paying for them, because they don't just appear on your bookshelf without work performed by a lot of people, whether that work is direct (effort) or indirect (funding). Free dhamma books are no more cost-free than those you pay for... it's just that they're effectively being purchased and subsequently gifted by the donor(s).
Indeed the Dhamma is the greatest of all gifts, but the cultivation of unwholesome mindstates rooted in conceit are detrimental to the individual and any attempts at dhammadatu they may be involved in. Accordingly I hope this topic doesn't become a "my dana's bigger than your dana" discussion as there's something distasteful about such comparisons, quite probably because they are the Dhamma being used for personal gain (e.g. pride, recognition, righteousness), which is precisely what the Buddha was trying to avoid in the first place with his actions.
"Having understood name-and-form, which is a product of prolificity,
And which is the root of all malady within and without,
He is released from bondage to the root of all maladies,
That Such-like-one is truly known as 'the one who has understood'." (Snp 3.6)
"Whether I were to preach in brief, Sāriputta, or whether I were to preach in detail, Sāriputta, or whether I were to preach both in brief or in detail, Sāriputta, rare are those who understand." (A I 333, Sāriputtasutta)