Yeah, I get that but I’m not sure what you mean by the actual moves you do. Having never stepped foot into a CrossFit gym I’m not familiar with the lingo. Since I generally do cardio before lifting that acts as my warm up.
Joint mobilityIt's helpful to me in that I have arthritis
Examples: hands just above knees, bent, simple circular motion one way then reverse. Hands encourage range of motion. Then for hips... weight on one leg - forward backward swinging action, move to crossing in front then in back. (this one really helps me and I do it before I go up the hill). There's bunch of others. Wrists and neck, etc.
Crossfit doesn't do cardio, in theory. Lifting tends to be limited as in one lift maybe two after a warm-up. Running is often part of the WOD - "workout of the day". So there is cardio, with more intensity. A WOD tends to have three or four elements, one blending into the next. Something like (kettle bells, push-ups, 200 yd fast run) x 5 maybe 10. Or (Wall ball, pull-ups - kipping, run 400) x 5. Or (5 deadlifts, 10 front squats and 12 burpees) x 8. All done on the clock.
I just made those up as examples. The WOD is for conditioning. There are standards and they remain the same most of the time. They are often named after women which is somewhat odd. The most famous is Fran: 21,15,9 pull-ups (kipping) plus thrusters (front squat to overhead with 95# for men). That time is kept world wide. It's killer.
One thing that I was surprised by is the strength gained by doing only one strength feature per day. I found strength gains throughout the body with the serious lifting.
Crossfit puts the hammer down!