Yeah, i do this way always , but maybe i don't get write it correct in English (not my born language) Let me try to change a chapter:
The way you described used by me all the time, line touches polygon in two points where it can be cutted and worked on forward very well (anyway thanks!)
But, if you draw a line that touches multypolygon - cut tool ain't works in places it touches multypolygon (not allowed - showed as gray)

Thanks , i will try it 👍