I play in a lot of tournaments every year and I see people keeping score on the course scorecard instead of the official scorecard all the time. I also know of more than one DQ because of transposition of numbers when filling out official card.
I do not do it. I keep score for whomever on the official card and record mine on the bottom. Just the way I will do it. I am ok with people keeping scores on a course card IN ADDITION to the official card if they want to just to verify everyone’s scores. But, don’t only do it and then copy scores over. Leads to mistakes.