PBS itself actually could do without the public funding it's such a small part of their budget (but also the federal budget) and the same for NPR, but often individual stations are a different situation, although any attached to a major university almost never need money and are already run as if trying to squeeze every cent of profit out of its production more than any "private" broadcasting corporation I've ever seen. Especially since they use slave student labor.
Individual shows are often a different situation for a differing reason, most things are not actually PBS/NPR productions and thus receive little to no financing from the parent corporation, many of the PBS branded shows actually get like a tiny cut in exchange for the PBS branding which is a normal thing in TV show production for networks. Some of the biggest franchises like NOVA and Sesame Street are funded and produced almost entirely off book because PBS historically can be stingy with promised resources, demanding of content control and makes unwarranted claims on profits. Which is a normal thing in TV show production for networks.
