The VAST majority of people who want to have PBS type programming can get it without PBS. You still have not provided a need for it.
I'd like to address this claim. Once upon a time, cable TV claimed it would provide alternatives to the kind of programing PBS provided in primetime. Science and Nature. Cultural shows. Historical documentaries, etc. So what is the status of those channels:
Bravo: (Movies and culture) The occasional movie and lots and lots of "reality shows". Some originals, some reruns of network or their own. (Their "flagship" show is the "Real Housewives of somewhere" franchise.
Discovery: (Science, nature, and learning) Cheap "reality" shows.
Smithsonian: Low budget series of "documentaries"on themes ("Mighty Planes/Trains/Cruise Ships"), Air Disasters
A&E (named for "Arts & Entertainment): Whatever resemblance it had to "arts" name was gone by the mid 90s when it was the "L&O" channel.
History: While it still did a lot historical content it became known as the "Hitler Channel" for endless WW2 documentaries plus ancient aliens. Hitler has apparently been defeated (or the WW2 watchers have all died off) replaced by paranormal content.
Science: probably fallen less than some of the others. Some of the content seems a bit sensationalist. I don't know the quality. (Several years ago I was eating in the bar area of a local restaurant and they had a big TV that sometimes showed sports, but that night they had it on the Science channel and I knew about half of the people in that particular doco.)
"Nat Geo": a cross between today's Discovery ad Smithsonian channels.
Another feature of PBS has been to show British programming. So, what about BBC America? The next 48 hours alternate between a "Bones" marathon and a "Law&Order" marathon. Most of the programming is American TV and movies these days.
The commercial channels that at least tried to focus on parts of the PBS portfolio have all failed to continue to due so, some have failed completely. (Discovery, History, Bravo, Smithsonian, I'm looking at you.) The notion that they are a good substitute for PBS might have been plausible 25-30 years ago, but not for some time.
I don't watch a lot of PBS these days (a few hours a month), but it is more than the rest of those cable channels combined (unless I spot a good movie on BBCA).