Trimmed surface to untrimmed surface

Agonizing question about trimmed surfaces.

I have read some threads, but did not find desired information.

After the operation 'Split surface' obtained parts is not always are suitable for further work. If I am not mistaken, all scraps are contain control points of the original surface. It involve smth problems with divide survace, isotrim, etc.

Possible solution - to rebuild the surface through the Edge Surface, but the presence of point of division on the outer edges does not allow make this without a dance with a tambourine around the selection and connection of curve's pieces with a further rebuild.

On the other hand, there are curves, which was cut surface. You can organize Sweep2 (With luck, it may be Loft), but again, we have to find the intersections, cut off, choose the section curves.

Are there more rational ways of reducing trimmed surface to untrimmed surface condition?
Is it possible to do this without rebuilding of the surface?