Good stuff. A few months ago I was on board an AA767 on the SFO-MIA run and we experienced exactly the same. Cleared for take-off on 1R, clearance cancelled for traffic landing on one of the intersecting 28s, exit to the right, back on to 1R and cleared again for take-off. It must happen quite often.
That's because the pilots took a little too long to spool up the engines or took a leisurely time taking off. By that time the narrow window of opportunity closed, as the aircraft taking off has to clear the intersection before the aircraft lands on the 28s.
Sometimes the taking off aircraft resumes their take-off roll from the stopping point or goes back to the line.