My apartment complex (in NY) works as follows. They pay Time-Warner cable for service, but that just means coax to each apartment and a basic signal. No cable box, but you can get CNN, C-SPAN, al-Jazeera, basically all over-the air channels, NY1, etc in clear-QAM if you hook up any digital tuner. Internet is separate as is phone service (get both of mine through Verizon).

Dropping cable service wouldn’t affect pricing for phone and Internet — the bundles aren’t appreciably cheaper in my building than in any other NYC apartment.