Abaft streaming is nearly exclusive territory of dedicated minesweepers. That, because those vessels have the needful otters and such to keep the sweep gear out of the screws. Which would be a difficult task on a DD or the like. Which is why the BBs, and cruisers all had either a fixed shoe or sliding she rigged to the forefoot.
Of course, the real problem with a paravane sweep is that it can only affect floating moored mines. Magnetic, sound sensing, command detonated, and the like will not be bothered i nthe slightest (barring grounding the sweep wire, but that is bad, very bad).
Now, paravanes bow shoe mounts do have an appeal to thos officers convinced that EM morale requires whitewashing rocks and similar endeavors. This, as the chained to and through the shoe need hoisting out and being cleaned of weeds and the like, with chipping, priming, and repainting those chains.