There are a few well-published occasions where a "pay what you want strategy" has worked very well. In music, artists have offered their product for download in return for a payment of the customers choice. Having customers pay for downloaded music, or not, works because the cost of a download is virtually nill, and anything an artist may receive for an album or a song is better than what they would receive if it is pirated and better than the minuscule compensation they receive from the music streaming sites. But for artists, there is another variable, the network effect. As an artist, you would want people to listen to your music, to talk about you, to talk about your music. For your band or you personally to become a brand. To use the brand value to drive visitors to the concerts and shows. So a "pay what you want" model for an artist has little to do with making profits on the thing you sell.
Museums and some similar organization "pay what you want" strategy where they "suggest" a donation. You don't have to pay it, but I suspect you would feel like a dork if you did not.
Then finally, churches often have an honor system where you can pick up a brochure or some information about the church in return for and also suggested a donation. And there are other special cases where the cost of actually having a sales person or method is more costly than products that are sold.
What these examples have in common is that the marginal cost of one more sell, is, well, marginal. Meaning that the cost of one more download, that the expense of another museum visitor or another flyer is virtually nill, and therefore the expense of those who elect not to pay is marginal. Simply, those organizations who choose a pay what you want strategy can assume the small cost of those customers who do not pay.
A particular case is some food charities, those of the kind who provide cooked food for the homeless. Some of these charities also have a "pay what you want" pricing structure where the aim is to support the cost of the expense of the food and rather than to make a profit. To contribute some cash to lower the organizations' loss. Many companies have an honor system for cookies or other treats available in their kitchen. Cheaper for the employees than a vending machine. Sometimes it works, sometimes it does not.
So, should you adopt a "pay what you want pricing policy?" In one word, no. Unless your business is one of the special cases above where you may have other primary goals that just make money on what you sell and where the marginal cost is so low, you can absorb the cost of those who elect not to pay (or to pay so low amount it does not even cover the small marginal cost.)