In the case of Long Island, I think the station is focusing on listeners who still use OTA radio and who are in the ages local accounts want to "invite into their store" or who might be homeowners needing repairs or a new floor or whatever. I think they are targeting both listeners and advertisers with the right demo focus.
Stations who are targeting local advertisers vs. agency do program different. A good example of one I am aware of is in Lake Charles, LA. KHLA The Lake has been doing Classic hits for 30 years. They usually lead the market and have almost no national advertising.
It appears the station is currently using premier networks in some dayparts, but during the 2000s was a lot of Middle of the road music. Some crossovers from country and a little Cajun thrown in once in awhile just to keep it feeling local.
I owned a movie theatre in Lake Charles at the time. KHLA was AWLAYS broadcasting from some local event or business. The station broadcast live from the theatre front lawn next to the road. Hundreds of drivers would pull up, drop a toy (Toys for Tots) in the giant bin and they got a pair of movie tickets, dinner at one of many restaurants and free station merch. They had this kind of activity down pat. They did it all with nobody at the station. During afternoon drive, the automation would go live to the announcer for 60 or 90 seconds after every two songs and after commercial sweep.
The station was hyper local, did a LOT of remotes, and could be heard in almost every office, or small business all day.
I did a halloween tick-or-treat promotion with KHLA and the local cable company. We had THOUSANDS of folks turn out at the the theatre for free trick-or-treating. Because of the crowd and the weeks long build up for the event, the local TV station was there and the local paper (front page the next norming).
So, my rambling point is if the station does not care about national advertising, they are free to program a station that the locals will like and hopefully the local advertisers will support.