Those donations could then be used to hire full-time developers, and work on the kinds of software that is currently not well served by open-source (TurboTax replacements, games, office software).
Just as with public radio or podcasts, the price signal of donations would encourage certain kinds of products to be produced according to demand instead of enjoyment or itch scratching, but the end product would still have the benefits of open source, no license keys or DRM to worry about.
I expect 99% of people would freeload as they do with public radio, but that's ok, even a small participation rate could result in new kinds of open source software being produced, and a sustainable career path for creators.