I"m not sure I understand the methodology but if I have to KNOW the location of the points, this just seems like an arguably more complicated way to find your position using re-section.
Your argument seems to be that you'd like to do some piloting without using any known reference points, and since the pelorus can't do that, it's not useful. Doesn't all piloting (in a sense, all navigation) involve finding your position relative to objects whose location you (or some device of yours) know? If you use compass bearings to get lines of positions to fixed objects like channel markers or recognizable points on shore, these are points you can locate on your chart. Ditto for circles of position found using relative bearings.
As an example, earlier this year we did a trip to Friday Harbor on San Juan island. On the way we only used compass bearings to take fixes. I found the bearing to recognizable objects: the breakwater of my marina (just about due north of my position most of the time), lighthouses on Patos and Saturna islands (to the south), smoke stacks near Bellingham, WA (more or less east), etc. I used bearings to these objects to draw lines on the chart, and where these lines intersected was approximately where I was. From there I knew what course to steer to avoid shoals, tide rips, and other hazards and get to my next destination (entrance to President's Channel). As the trip progressed I had to switch to new landmarks like Flattop Island (SW), radio towers on Orcas Island (NE), O'Neil Island in Rocky Bay (SW), etc. All stuff that's marked on charts and that I think I can recognize from the boat.
Using relative bearings to find circles of position is exactly the same thing, except that instead of drawing lines on your chart, you draw circles. I didn't really know about circles of position on that cruise, so I didn't try to use them, and yes they are more work than lines of position.
However I can see situations in which they might be more useful. Just as you use danger bearings to avoid hazards, you can use a danger circle. For example, imagine you can find two points with a circle through them such that some shoal water just fits inside the circle. If the angle between the two points that gives you that circle is thirty degrees, then you need to make sure the angle you measure with your pelorus or sextant never gets bigger than thirty degrees, which means you have gotten inside the circle.
Basically the compass and pelorus both provide some sort of line of position. Sometimes one is more useful than another. If nothing else, having access to both will add redundancy to your piloting and give you more confidence in your fix.