My initial thought is that it may lead to many customers with a $1 payment, but some may pay derive more value, therefore paying above your fixed pricing tiers.
Thoughts?
If it's "this is a great marketing strategy" well, um, maybe but hopefully you have better ways getting your customers to hear of you.
If it's "this would be a fair way of matching value provided to cost", well, um, maybe but I think you're still better off naming a few different price points to cover your intended customer segments.
If it's "I don't know what this is worth, you decide", well, no, just no. Man up, make a decision and name a fair price. You don't get to cop out of making the hard decisions if you want to have any hope of making money. Also, if you don't know what the service is worth then I strongly suspect your customers won't either and perhaps you don't have a viable business.
In the examples in description, insurance and travel, there is a demand seeking a supply and the supplier gets to choose if the price is right to fill their void.
Good thought on the band's album donations.