Yes, you keep getting increased responsibility and it is expected that you give the younger guys a chance to gain experience. However this is after several years, not over a short period of time.

If you go the CRO route expect to deploy 2-3 times with a team, then deploy as a commander and stay in the JOC to control and advocate. You will definitely get lots of leadership experience but their main role is not to be in the shit. It happens, but not often. Honestly, in my experience, officers in general don't see the front lines of battle. If you want to see combat, go for the rangers… they see a lot. If you want to save lives and occasionally see combat, be a PJ.