If the question is, why is there no radar coverage over the ocean, the issue is "out of range" rather than "below", and the secondary answer is "we don't really need it".
Bear in mind there are two radar systems, "primary" that relies only on reflection of the radar signal from the target back to the radar installation, and "secondary" that interrogates the onboard transponder to identify the target, and the target actively responds back to the radar installation.
In addition to the line of sight factor, near the ground the primary radar will be overwhelmed by "ground clutter", reflections from objects on the ground that aren't aircraft. As to distance, not only is the curvature of the earth a factor, but the radar return is no longer strong enough to be picked up by the ground station and separated from the background noise.
Shipping would not be helpful because there is not enough of it to provide anywhere near reliable service, let alone that they are not interconnected and you would have to rely on some transmission medium such as satellite to get the radar returns to the controllers, and there isn't enough bandwidth even if you had the interconnect.
We use the old fashioned way, position reports and generous separation, to handle oceanic traffic. It works for the amount of traffic that needs to be handled. Also, the aircraft have TCAS onboard so they can keep track of one another.