First, there is always a "safe limit" for anything. If you don't understand that, you don't understand the "fineness" of the granularity of matter.
Second, small amounts of CO will NOT do any permanent damage to the human body. Larger amounts may. (I would call death permanent damage. Brain damage is also possible but certainly NOT inevitable.)
Third, the effects of CO are not cumulative over large spans of time. They may be cumulative over short spans of time.
Fourth, the binding of CO to hemoglobin IS a reversible reaction, but it does take a while for it to occur.
CO is very toxic. If I recall correctly, the lethal dose 50% (LD50) is 1% for one minute.
I have some experience in this area as my brother was seriously exposed to CO a few years ago. I feel that CO is such an underrated danger that this past year, I purchased 50 CO detectors that are about the size of a key chain. I gave them away to all my family members and employees. I picked the one I did because it gives readings in trace amounts as opposed to just giving an alarm. My employees could be exposed to CO in the factories where they do work or even in hotel rooms... yes, this past year there has been quite a few incidents of high CO levels in hotel rooms due to pool heaters etc not working properly.
It has been more than 12 years since my son got carbon monoxide poisoning, he realized before he passed out what was going on and was able to crawl to a place where someone would see him and call for help. A co-worker who was with him said that his heart was jumping out of his chest.
The ambulance crew gave him oxygen and he was in the hospital for around 30 minutes before he came to and told them what was wrong they checked and said that he had what should be a lethal dose He recovered quickly and as far as I know has had no permanent damage. The Dr. said that he had the heart of a horse because he shouldn’t have survived.
Some years later he had to have a hernia operation and the medical staff was amazed that his heart rate was only 40 beats per minute and when he was in the recovery room the alarm was constantly going off, they thought he was a marathon runner or something.
What I said too, but don't expect anyone on this forum to ever admit they're wrong.