There are a few reasons why pay as you want could be profitable.
Pay as you want allows for price discrimination. Normally this means companies try to extract the most a customer would be willing to pay by offering different services, such as extra legroom on planes, for example.
Think about how much you would pay for a smashed avocado breakfast. For some people, the answer is A$10. For others it is A$20. A restaurant that prices its smashed avo at A$15 may be losing some customers (those willing to pay only A$10) and also fail to capture the full value from other customers (those who would have been willing to pay A$20).
By allowing people to pay as they want the restaurant can successfully cater to both types of customers.Price discrimination occurs when a firm sells the same product to different customers for different prices, and when those different prices do not relate to differences in cost. Is a voluntary purchase scheme (or 'pay-what-you-want pricing', if you prefer) an example of price discrimination? On the surface, it would seem so - certainly different customers are paying different prices for the good or service. However, I would argue that voluntary purchase schemes are not price discrimination, for two reasons.
First, with price discrimination, firms must have market power. That is, firms must have the power to set their own price. If you let the customer set the price, then as a firm you've given away your market power. It is the customer who has the market power in a voluntary purchase scheme (which explains why many customers will choose to pay zero).
Second, with price discrimination the firm is looking to extract additional profits by charging a higher price to consumers who have a higher willingness-to-pay for the good or service (or who have more inelastic demand for the good or service). In order to do this, you need some way of sorting customers into those with high willingness-to-pay and those with lower willingness-to-pay. Movie theatres do this by sorting the students and seniors out from the other adults. Airlines do this by sorting those who buy a ticket shortly before a flight from those who purchase well in advance. Online sellers might be able to sort based on the data they have collected about you. And so on.
However, with voluntary purchase schemes the price that the customer actually pays need not depend on their actual willingness-to-pay. It is based more on their 'willingness-to-share' with the seller. It is based on their altruism, or how pro-social the customer is, or social norms, or moral incentives, or some combination of all these things. So, there is no certainty that a customer with a high willingness-to-pay will pay a high price, while a customer with a lower willingness-to-pay will pay a lower price. And so, 'pay-what-you-want pricing' isn't price discrimination.
Despite this, Camilleri's article is worth reading, because the voluntary purchase schemes is a fad that has been coming in and out of fashion on a fairly rapid cycle over the last decade or more. Although, that may just be because the sellers who think it is a good idea run with it for just long enough to run out of money and go out of business, and then there is a little break before the next idealists try it out.