You called? I usually don't respond to stuff like this when I have work on my own that needs attention,
but I'll make an exception for this one. As I see it, the original National Educational Television and Radio Center (NETRC) would be a start, in all its controversy. What needed to happen in the 1950s and 1960s was to get more funding and exposure to what was then called educational television; radio never really registered in people's minds until it got forced by public radio advocates.
Having said that, I am of two minds about this. If you want a pre-WW2 POD, the easy way would be to avoid the disputes by the NCER and NACRE, which could thus allow a non-commercial "educational" system to be set up integrating both the separate non-commercial system approach of the NCER and the cooperative broadcasting with commercial stations approach of the NACRE. (The public broadasting trade journal
Current has
a great section on this dispute - particularly
here - which is worth reading.) Believe it or not, but originally - until the networks got in on the act - broadcasting in the early days was non-commercial to begin with, but it only really faltered when the Federal Radio Commission was biased in favour of the networks in opposition to existing non-commercial stations, such as WCFL in Chicago or one station in New York City set up by the Paulist Fathers. The original setup of the FCC could have potentially provided for a stronger voice for what was then called educational broadcasting, but alas that was not to be, leaving non-commercial radio to languish on like some ghost, allowing the networks to rewrite history to emphasis themselves over the non-commercials. For a post-WW2 POD, it's more difficult, but given the Ford Foundation's role during the early years of educational television and its emphasis on giving public broadcasting national status, it's certainly not inconceivable to have both educational radio and television advocates join forces (if the TV people do not try to be so dismissive of radio) to create a format for public broadcasting on their terms. Even better if the original excise tax originally proposed the Carnegie Commission in their report on public broadcasting was retained.
Either way, what the end result will be, the United States being the United States, is not going to be something akin to the BBC or CBC/Radio-Canada. Instead, what might end up happening would be a cross of the German
ARD model (where regional public broadcasting companies pool together common resources to form a national system) and the Dutch
NOS/NPO model (where member-based broadcasting associations, representing different aspects of the multicultural nature that is Dutch society, are allocated airtime to broadcast their programming). Thus, in some ways both television and radio would resemble PBS and NPR, but the ethos for the stronger system here is the diversity of voices within the system. In order to get any "fourth network" off the ground and deliver compelling programming that would make this system fit the OP, you need to make the general audience feel like they "belong" to the network because the programming speaks to them. Let's be honest here - from the beginnings of educational broadcasting in the '20s all the way to at least the mid '60s, much programming on educational stations were largely dry, academic, and not really engaging. The only that would change is if the stations themselves begin producing more programming that would usually be imported from the BBC - things like drama, or comedy, or general entertainment, and the like. In many ways, many of the same problems afflicting the CBC also afflict the existing public broadcasting system in the US, albeit even more so in OTL due to its niche role in the system. You have to give the system breathing space to produce such programming, even if it also decides to choose to import similar programming from overseas. IMO, a hybrid of the ARD and NOS/NPO models is the only realistic model for the US - all the more so since ARD was, in part, founded by Americans in the immediate aftermath of post-war Germany.