NPR and PBS represent benchmarks for what programming can be when the producer and distributor are less concerned with profitability than they are about content.
That is not to say that ALL programming should be of that type. But when the mood strikes someone who aspires to be a journalist or screen-writer or artistic producer, they should have something contemporary to draw from that they can set their sites on getting as close to as possible.
Do public broadcasters have any sort of obligation to crank out new content to fill up the 24-hr broadcast day? I don't think so. We did just fine in the old days when the broadcast day went from around 6AM to 11PM or so. No one died as a result, and we had plenty of fine "classic" programming. And certainly, if one's particular interest in public broadcasters is for children's programming, you obviously don't need anything beyond those hours.
So there are certainly possibilities for cost-reduction, but eliminating public broadcasters as an entity is simply foolish.