Yeah, in reality none of them should be going on away missions unless they are diplomatic in nature. Hell in the CMO's case, sending your chief medical officer on an away mission to render aid is like sending a hospital's chief of surgery out in an ambulance
When you call someone a chief of something like security, engineering, medicine, then they are administrators & top specialists, only to be called away in the rarest of circumstances, not to make some goofy Pakleds "Go"
Frankly, chief of operations shouldn't refer to the inner workings of the ship. That should be like chief of facilities or something comparable. Chief of Operations should be the person in charge of all away mission ops, whether science, militaristic or technical related
& if the captain is the designated diplomat, then he actually has more need to go away then the XO. These are all jobs that need to either be more specifically designated or for the sake of tv, need to actually be more like TOS had it... ambiguous