Why can't I get PBS streamed live?
Because they're a national network. They don't directly broadcast to anyone. They provide content to local affiliates, who then handle scheduling and intersperse it with local and syndicated programming. They don't directly broadcast a "pure" PBS national feed anywhere in the country because that's not their mission, so there is, of course, no national PBS feed. If you were to get a live feed it would have to be from a local affiliate.
The reason it's not available streaming is because you'd have to get your content from a local affiliate, who would need to make deals with PBS proper (who would, in turn, need to have deals with everyone producing content for them), and deals with anyone sending them syndicated content, and everyone producing content locally. That's a huge deal to set up. Potentially easier for PBS because they won't have to make the case about ad revenue online, but that's still a huge legal mess to get themselves into, because you better believe everyone will bring their lawyers to the table on this one.