Should an officer be allowed to continue to serve on Active Duty after being relieved from command?

Probably.

If they are incompetent to lead then there is no need for them. Anyone relieved of command should be separated at the same time.

Lead , follow or get the hell out of the way !

I don't know how it is in the other branches. But in Naval aviation unless you screen for command - you are a desk jockey and game over at 0-5. 0-4's do not command but are major department heads and compete with fellow 0-4's for the early promote ticket and a #1 or 2 fitrep from the CO - out of 5 LCDR's in the squadron. Once they make CDR 0-5, the real sweat starts to see if they will screen for operational command. (a squadron). IF they complete the squadron tour sucessfully and are the #1 or #2 out of all of the squadrons in the CAG (carrier air group) they promote to CAPT 0-6, and now again they sweat to see if they will screen for Major Command, a Carrier Air Wing job (CAG) or a deep draft ship (oiler etc) some may go straight to the Nuclear power command pipeline as a Carrier executive Officer. Now the competition for a star begins. 12 carriers - 12 CAPT's 0-6. Maybe 1 or 2 will get a star as a RADM. Non screen Commanders usually become Naval Air Station executive Officers . Non Major Command screen Captains become Naval Air Station Commanding Officers and or training command Commaning Officers.

You do not get relieved of command for minor things. If the DOD is feeling magnanimous, allow him to retire. If not at a minimum Article 15 him for the offence that got him relieved of duty and force him out.

NEVER......

The job of every officer is to command. It doesn’t matter what his assignment is, his first duty is command. If he is not fit to command he shouldn’t be an officer.

I think if the army implemented a plan for a new rank system after specialist not nudging a a solider to be an nco if he not a leader but still giving him the opportunity to rank up it would help the problem

So you mean like non leader NCO's and Officers like pilots, nurses and doctors? And any DIrect Input Limited Duty Officers. The Navy is clear on this you are a Line Officer or a Staff Officer. Staff officers can not take command of a ship. I am pretty sure Line officers that are releived of duty have no where to go. NCO's on the other hand probably retire. Never thought about it, or ran into it either.

I realize I am probably staying the obvious but if he or she should be allowed to serve and be paid until the investigation is complete and an outcome has been reached.