For me, there are two reasons why I don't use the C&J in my training at all.
One is that catching the weight overhead in a partial squat is not friendly to my shoulders or lower back, especially with doubles. If you have the requisite mobility, such as if you can overhead squat with no problem, then this doesn't apply to you.
the C&J would appear to have less risk
For the reason mentioned above, this has not been my experience, whereas I find the snatch to be a very low risk drill. After rotator cuff surgery (basketball injury) I was able to return to snatching long before even holding a bell comfortably in the rack.
Two is that dropping under the weight to catch it doesn't feel good to me and is counterproductive to my goals. I want to focus on explosive extension. Dropping under the weight doesn't necessarily preclude maximal explosive extension, but in my experience it can distract from it.
The snatch is a mainstay in my training, both for its benefits and because I find it a very enjoyable and satisfying movement, which is a big factor in my choice of drills.
When I want to do something akin to a C&J, I do double push presses with weights light enough to propel ballistically to lockout without having to press them out much or at all. This way, I am only dipping with the bells in the rack, not overhead, and I feel like it is a sweet spot for maximum power (subjective impression; mechanical reality may or may not be different) -- less mass, but higher acceleration/velocity, the dip and drive is very quick, and I can really focus on powering through full extension without having to think about a second dip. This style of push press also seems to have a lot of carry over to my main recreational sport of basketball.
I also do a lot of double cleans as a stand alone drill, one that I think is very underrated and underutilized.