Having to keep and sign a scorecard in a professional event is draconian. There aren't any other sports like that.
It's like asking a cricketer to give himself out or a bowler to call a no ball.
We have the technology available. Each group should have an observer that reports any instance of possible rules breaches to a referee for video referral and to keep score for the group. It's the only way to avoid this sort of thing.
Can you imagine how much time that would add to a PGA Tour Event.
"Ladies and Gentlemen we are waiting on the 8th Tee with Kevin Na and Jason Day, as the footage is reviewed of the last hole played, where Kevin, may or may not have taken, wait lets count them, 6 practice swings, per pre-shot routine, (that's before and after he checks his alignment on his approach shot) while Jason may or may not have incorrectly marked his ball on the green. We appreciate your patience and will be back after this 5 minute commercial break"
"Welcome back, and no Jason has not incorrectly marked his ball, but Kevin has been given a warning and may be put on the clock for taking 25 minutes to play the 7th, which he did in fact birdie, back to you Nick"