Forget the now-meaningless terms of "live" and "local".
In the past, we were "live" because we did not have the technology to let programming be created more efficiently.
And we were local due to the costs, quality issue and time zone differences in the US.
None of those are issues now. A talent can put together the content of a 4 hour show in less than an hour if they do adequate prep. The Internet and cable TV, among other things, have pretty much leveled regional differences in tastes within specific formats.
So it's better to do what TV discovered back when they put Steve Allen's creation, the Tonight Show, on the network in 1954. They knew that being in a media center where there were stars and characters available for easy access trumped being in Macon and having access to the local sheriff.
In a "world" which is defined by the Internet for nearly everyone, your criteria is out of date and has been for decades.