Any exercise or lift can be made better for the individual. Exercises can be more geared towards strength and stiffness while others are for better movement. The setup/position and execution will guide what muscles are used and the qualities that are trained.
Most people will still need to train push, pull, squat, hinge, core, and power. The exercise selection can be different though.
Some exercises need you to be very stiff all over and just move your arms or legs. Bench press, back squats, deadlifts and any heavy lifts… you probably don’t want to rotate or bend while doing these. You’ll lift more weight and get better at producing force. These are good exercises to gain general strength and power. Also, just good for beginners because they tend to be more simple. Stay put, get tight, move up and down.
But many people are already very stiff and strong, especially enough for wrestling, a sport that demands a lot of movement and quick position changing.
Being able to rotate is the gold standard for movement. This is when the sides of the upper or lower body are doing opposite movements. Pushing/pulling and squatting/hinging are opposite movements, being able to alternate these patterns easily is important.
An easy way to incorporate this into your lifts is through alternating arm action and/or a split stance. One arm pushing while the other is pulling would be rotation of the upper body. Single-arm pushes and pulls… think dumbbell presses and cable rows. A split stance such as a lunge would be one leg back and one leg in front is rotation of the lower body. Split squats, lunges, single-leg squats and hinges.
It might not be worth it for you to switch your main lift, but one of your accessory lifts would be a good spot. Still do heavy lifts with two arms or two legs, just do an alternating arm action or split stance movement after. This way you’ll get the best of both worlds. https://www.instagram.com/p/CPlrwA_h4Lj/
If you are very strong and stiff, it may be worth it to incorporate more rotation as that might be the main limiting factor for you when it comes to performance. But for most people who may have just started lifting weights a few rotation exercises is all that is needed to stay feeling good. https://www.pullmanperformance.com/post/wrestlers-stiff-vs-loose Try out some new exercises, see what happens to your strength, stiffness, and overall feeling.