CARES does not have a crotch strap because the FAA was concerned that given the particulars of airplane movement the strap itself could cause injury. In their testing the FAA found that if the CARES straps and the lap belt were tightened securely, slipping beneath the belt is not common. With that said, children grow and develop at various rates including the ability to sit upright, unassisted, which is necessary when using CARES. You can determine what’s best for your child.
If the CARES straps and seatbelt are tightened securely and your child still slips down, then it might be helpful to use a thin piece of rubberized mat (like shelf or sink liners) and place that underneath their bum. You can also try putting a bolster (or rolled up jacket or towel) under the backs of the legs. This helps bend the knees which can also help prevent them from slipping down.