To add, having thought a bit more about it, I really don't think that 'offenses' that are not quite bookable offenses should be totted up.But persistent low level fouling does break up play too much, and is worthy of a yellow in my opinion. It's a good rule, if somewhat subjective.
Your reasoning is that the cumulative effect is to break up play. I agree. But that is not an offense.
Likewise, Fulham, Newcastle and Villa suffering from multiple off-the-ball player malfunctions, resulting in players sitting down till the ball is kicked out of play, is designed to break up play. But no player ever gets carded for dubious malfunction on the basis of 'totting up' let alone on the basis that there is an actual rule that has been broken, when this happens.
In fact in the latter case, the referee has no requirement to stop play for anything other than a head injury, yet none, ever, in my recollection, has waved play on after a player (normally on the side of the malfunctioning player, but quite often the other side) has kicked the ball out for a throw.
I can live with subjectivity as long as it is clearly and unambiguously enshrined in law. It would need to map to a notion that the judgement of a referee is final when the actuality is unclear. However I still struggle with the idea that a non-bookable foul can become bookable if it is part of a series. In effect the referee is being allowed to attribute the sequence of non-bookable fouls to a conspiracy.
So, no I don't like it.
And back to the time wasting by injury faking, if you accept a totting up process for non-bookable fouls, why not allow a totting up process for a suspiciously-improbable sequence of sudden off-the-ball malfunctions? I can't see that ever happening. That said, if the refs ignored all off the ball malfunctions that are not head injuries (or Erikson-style collapses) then this problem would disappear. I seem to recall we discussed this at length after a Newcastle or Fulham game passim.
In short, the referees are wankers.