Are you asking if you sign-up for giga-fiber, would you get an ONT or a DOCSIS modem?
I think FTTH would have its own NID (aka slack NID) or a newer, modified, larger NID to not only preserve the existing coaxial but also some slack rigid-fiber. If you get FTTH, fiber would terminate somewhere inside your house.
I'm not sure if that termination point and the ONT are the same thing. If not, what connects the termination point to the ONT...a run of flexi-fiber equipped with a snap-jack?
Cox will install the ONT at the closest electrical outlet near the NID.