I actually thought it went on too long for THAT time-period of boxing, but to answer your question I think it'd be stopped much sooner today.......it's been awhile since I watched the fight, but I believe when Paret turned his side (almost his back) to Griffith the fight should've been stopped......but the punishment went on for a quite a bit after that.
It would be stopped sooner if the referee could get between Griffith and Paret. Part of the problem was that Paret's arm was caught in the rope and Griffith was hard to control.
.............Goldstein was negligent; pretty simply put, but it's true. Paret was allowed to absorb a sickening amount of unnecessary punishment, even by today's standards. That said, Paret took that fight not very long at all after the Fullmer pounding. Had Griffith not caused the damage he did (however unitentionally), Paret might very well have come a cropper against the next opponent he'd have faced.