Personally I always found CS7 awful. It took them years to sort out the deadly junctions at Oval and Stockwell and I've never found the bits around Clapham, Balham and Tooting not to be blocked by parked cars and delivery vans. That and it seems to attract a fraternity of wannabe TdF riders. There didn't seem to be much difference to the A23 in my opinion, other than the blue paint.
As to the petitions, they just regurgitate the same shit every time (for 20mph zones, home zones, street closures, you name it). But the moral of the story is to never pitch these change as 'for cyclists,' they have to be framed by broader benefits. Which isn't even difficult, no one actually likes being run over or breathing out of an exhaust pipe. Sometimes I think they set up these things to fail.