Cut loop to two equal parts...

[micheus]

we do select all parallel lines along the tube-like object... then we do click 'cut in the middle' and, voila, there appear vertices in all the cut points...

It seems simple said this way, but I have doubts.

In your illustrations using ropes it seems you expect to get a new loop cut parallel to other edge loops, but that would be not possible (maybe for the first one). If we want to cut the edges taking in account its length then we can't expect that.

Just to illustrate I made this picture:

In the picture, taking in account the edges' measurements I found the vertex for the top and bottom edges which are in the middle of those edge segments. In the right image you see the that cut respecting the equal length cannot be done parallel to the edge loops.

What I think is, we can find the middle or n-cut based in the edge segments length, but it's up to user decide how to use it. There is no warranty the result will be what he expect.
If he wants to get the cut parallel to other edges loops, then he probably will have to select only one edge segment for measurement and use other command like plane cut to complete the operation.

In the past, when I needed this kind of operation, what has passed in my mind was that by selecting edges loops we would get the middle point for each one and build a segment that could be cut and these points (from cut) combined with some normal vectors would be used for make cut in the object. But, in the same way, that would not produce a good result for all situations.

Just my thought.