Because there's probably more legal hassle to try to discontinue pasenger service on the line than there would be to just run one train a day to make everything legal.
They've already discontinued all the stops along the way. This is about the most minimalist service they can offer and still keep the line open.
Also, I have no idea if there is some sort of legal issue for the NY&A handling freight along there. If the LIRR has no passenger service and they can't qualify keeping the line open to run freight as they no longer run their own freight, then, perhaps, the line may be considered abandoned, in which case the NY&A wouldn't be allowed to service the freight customers along there. I'm sure an ownership issue is involved as well.
Not really sure . . . just possibilites running through my head but I ain't no lawyer!