I would be extremely concerned about the ability of such a telescope to make adequately precise measurements, given the motion of the water. The leading radio telescopes have their mirrors and receivers very exactly aligned. For example, Arecibo's Gregorian dome could be aligned with any location on the order of millimeters, while the Green Bank Telescope's mirrors are aligned to the tenth of a millimeter. I would certainly be concerned about replicating this performance in the ocean. It's fine for an aircraft carrier's surface to wobble by a couple orders of magnitude more than that; it's less so for a world-class radio telescope. I would expect to see mirror deformation and pointing errors due to the motion of the water.
There's a basket of additional logistical issues - constructing the telescope on water, transporting personnel to and from the structure, combating temperature variations, protecting electrical components from short-circuiting, staving off large waves, etc. All of these drive up construction and operating costs, and astronomers aren't exactly rolling in cash.
I can admittedly see two possible benefits from the plan. First, radio frequency interference (RFI) from artificial sources would presumably be nonexistent throughout much of the open issue (although Connor Garcia makes the excellent point that the increased amount of water vapor could be problematic!). RFI is the bane of the radio astronomer's existence, which is why radio quiet zones are so important. As a counter point, of course, there are available formal and natural radio quiet zones which could be taken advantage of. Second, you could change the telescope's latitude, which would give it a wider range of sources. On the other hand, it's not as if any significant parts of the radio sky can't be seen by radio telescopes, so it's unclear as to the benefits of this.
Overall, I'd say that the precision issues outweigh the potential benefits. If the National Science Foundation were to fund future replacements for Arecibo, there are plenty of better options, some of which are already being planned. If an aquatic radio telescope were ever to be built, I'd guess that it would be entirely privately funded by a billionaire with money to spare who would be willing to take significant risks. I wouldn't complain about something like that, but at the same time . . . I think a conventional radio telescope would be a much better choice.