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

Kind of depends. I would suggest he get a new line of work.

The Navy has a system where they have a command track or staff track. Works well for them maybe other branches should consider.

Most of the poor leaders are eliminated by the promotion board. Twice passed over and you are gone. Most of the guys I knew that were relieved were not poor leaders overall but made a big mistake they probably would not make again.

Not everyone is cut out to be a leader, but in the military everyone gets an opportunity to lead. Those who are relieved often have other talents and if history is any judge, sometimes they can come back to successfully command. There were numerous instances of that in WWII.

Definitely not everyone can be a leader. There should be other positions that soldiers can stay at at the rank they're already at. They are good at their technical job so keep them at their place. There's no reason for new Joe's to take their place because they are excelling at their job. In my field we are so short on NCOs every E4 is going to the board whether they are a good leader or not. There's so many that shouldn't go to the board at all.

Hex

The problem isn't "Big Army" wanting people to strive to be leaders. The problem is people in leadership positions promoting or recommending for promotion those that aren't good leaders into leadership ranks and positions. I the Army had a fix for this that should be brought back, the Technical Specialist ranks. This woild allow the Army to keep good Soldiers that may not make good leaders.

My Army service is long in the past, but can tell you candidly in hindsight that I was a mediocre leader but was a very competent staff officer and worked hard at it.

Well, some of those officers are not yet eligible to retire, and get such positions so they can get to retirement. Partly, that's not fucking over people like happened to McCabe (not intending to discuss the validity of that firing, just an example). But it also means bad PR fades before they go. After that astronaut drove from Texas to Florida in a diaper and committed assault, NASA sent her back to the navy, where she flew a desk until retirement. By the time she got out, the press no longer cared about her story. Had the navy said "bye, don't bother to write", she'd have had no pension, and might have cashed in with a tell-all memoir trashing NASA and the navy.
Is it worthwhile to keep a lid on bad PR to keep them around? I say no, but I never had stars on my collar. I'd rather ask congress to authorize a special pension rule: if the officer is being court-martialed for an incident that gets them cashiered, the board can recommend early vesting, subject to the secretary's approval. An 18 year officer could then get a 45% pension, instead of being kept until they hit 20, still subject to the paygrade being determined based on the last paygrade they served honorably in (as in the general who had an affair in Italy, and got a colonel's pension).
If it's a case of the Peter Principle, I would support moving them to a new job and keeping them around. They can still contribute.
As for toxic leadership, I saw a lot of it, and have long wanted to see the investigative services go undercover at commands to look into it. For example, a ship gets a reputation on the waterfront, and soon, a new E-5 checks aboard. He may be a chief, senior chief, or even junior officer, but his paperwork from BUPERS show him to be the 2nd class the ship needed. After a couple of months, he can tell NCIS if the complaints about the ship are valid or not, and who is to blame. This would go a long way towards fixing tje hundred hour work weeks that contributed to the Fitzgerald and McCain collisions.
I think that toxic leadership is one issue, that really needs to be addressed, and that up or out is another. Line officers should have up or out, with the possibility of getting off that road into a staff or other support track where there's no pressure to advance, merely to continue performing. If you want to make admiral, or have a command, you have to accept up or out. If you just love your job, and don't care so much about making rank and being the big kahuna, you can escape it and keep doing your job.
Of course, I will probably never be in a position to implement this, just as I will not be able to make the services adopt tje 360 fitrep program they bandied about briefly.

Yes

As was said by my peers, not everyone is cut out for leadership. I have met quite a few people who were not very good leaders but were excellent instructors and matter experts in their field . As far as should an officer be allowed to remain on AD, that all depends the circumstances and should be judged on a case by case basis.

No

Absolutely. Now as for Enlisted they need to bring back specialists ranks.

Separate !!

I think that if you as commissioned officer or senior enlisted service member get relieved of command/duties you should be encouraged sometimes even forced to retire. If you get relieved of command/duties is pretty much like being fired or am I wrong ?

If you where around for some time like 21 years you experienced. Bad leaders. When I was totally frustrated. I'd say sir lead follow or get the hell out of the way.

Retraining might be in order if the officer has some level of competency

Bring back the old specialist rank structure!!!!

I wish it was that easy but yes, no one should just be passed along. I witnessed it all to often.

This should be a reason to separate an officer, not to make him someone elses problem.