I'm sure we're going to lose a lot of hyperlocal news and current event programming in Shreveport or whatever, but those programs have tiny audiences (even relative to their media market). Most of what we think of as PBS and NPR programming is delivered principally over the Internet now, not via local broadcast stations.
The problem is hyperlocal news is what keeps local government accountable. The internet has starved these local newsrooms to the point where NPR was often the only one left.
Local news is a much bigger and grimmer phenomenon than PBS.