To my mind, the zoo itself is not the issue with Chessington. The zoo areas are in places dated, but typically pleasant enough. Also, although they have all the usual animal park animals like Humboldt penguins, Asian short clawed otters, meerkats and a variety of uninteresting antelope type thingies, Trail of the Kings and some other enclosures have some more unusual fauna to enjoy.
I agree with most of the recent comments before mine. The park could combine animals and rides neatly if it was handled properly, but the planning restrictions and other Merlin parks not far away are seemingly being used as excuses to push the park further and further towards the animal end of the scale at the expense of the rides. Unfortunately it doesn't compare favourably to a full-blown zoo, and the queue times for the park's entirely inadequate capacity rides strongly suggest that the rides are still a much more significant draw for guests.
Cutting one side or the other is not the solution; either would likely be the end of the place. What I think is the answer is a swift but carefully considered rebalance of the park, with priority given to both new ride attractions and park infrastructure so that it can not only handle the guest numbers it gets, but actually impress them! An intertwined family coaster and rapids, as often suggested, would be a good start. If the themes for these new attractions could sensitively incorporate new enclosures for appropriate species into immersive surroundings, I think Chessington might then finally be on the right track after years of seemingly plodding along in a directionless manner.