For one thing, believe it ot not, not everyone has cable or satellite. Of those 1000 channels, how many have locally oriented programming that really means anything to your community? In my city, the local commercial channels have news shows a couple times a day where they pretty much repeat headlines from the local paper. They do a credible job with the weather but as far as any depth of reporting on local news & events, forget it. OTOH, the public TV station & NPR radio station have real and detailed local content for a signifcant part of their programming day and the national programming they carry is often of a type that is simply no longer played on commercial stations. They do have some ads but in length, quality, and content, they are nothing like the obnoxious advertising on the commercial channels.
If you examine the FCC policies and regulations it is apparent ALL broadcasters & spectrum users are subsidized, perhaps some less directly than others, but on the whole the system is very much geared towards providing benefits to business rather than the consumers. I don't believe that the small amount of federal funding public radio and TV receives is misspent. Public broadcasting provides a valuable service, at least in my area. If these stations had the plug pulled, it is highly unlikely that commercial broadcasters would step up to replace that.