"In other words, if the cost to serve a customer (support aside) is zero, the long-term price of the product in the market will be zero (because of competitive pressure)."
I can't think of any large scale operation where the cost to serve a customer is zero. Sites like Google, Facebook and YouTube have massive operational expenses that they struggle to cover with aggressive advertising.
Of course, the freemium model works very well for many companies. Nevertheless - "zero marginal cost" is an illusion.