In reading all the recommendations, I'm realizing that much depends on how much magnification you are happy with. If 7x does the trick for you, then no stabilization is required, and it's all about optical quality.
Personally, I have never found 7x to be enough magnification. If I'm overtaking a boat in a waterway and trying to read their name off the transom so I can hail them, I find that I'm pretty much on top of them by the time I can read it. Same trying to read the number off a buoy or marker. Or trying to read the air draft gauge for a bridge to see if you can fit under, or if you need an opening. 14x makes a world of difference in situations like this. But once you get to 14x, you will have enough magnification, but then movement becomes the limiting factor, and a nearly impossible problem when the boat is moving. In steps stabilization, and now you can identify boats from a comfortable distance, figure out bridges when you can still hold back and wait for an opening, and identify nav markers well in advance.
For all these reasons, I have found stabilized 14x (give or take) binoculars to be indispensable.