I've already stated that I regard the 3RR as unsatisfactory, underpowered because it tolerates a very high level of pointless edit warring. With the alternate interpretation, in my opinion, it's worse than useless, at the very best just a drain on sysop time. It would magnify the power of determined edit warriors by giving them carte blanche to perform up to three daily individual reverts on separate sections on the same article. If the alternate interpretation gains wide currency among edit warriors (and it's only a matter of time), the effects will be to intensify the problem that 3RR was intended to ease.
It has been my impression that the common interpretation of the 3RR (that it only involves the same piece of text), and its enforcement as such, has led to significantly less edit warring. Not perfect, of course, but better than it was.
Jay.