Probably depends on location.
In my location, back in the 70's when Taekwondo really started taking off, there were many more Kukkiwon certified instructors than not. There was one ITF instructor, but he ended up getting murdered. He was then replaced by another ITF instructor, who built up the program to the point where he became our state president because he had the most students. In the 80's, most of the instructors retired or moved away, including the ITF instructor, and taekwondo fell off. In the 90's, the ITF instructor returned and once again became our state president and I served as his secretary general. Around this time, GM Dae Sung LEE moved back to Hawaii after teaching at OTC for six years. We invited everyone to our meetings, whether tang soo do, ITF, everyone, offered them Kukkiwon certification, as well as training in modern training methods, for free. There were some hard feelings between certain individuals, but that worked itself out over time. Now the overwhelming majority from that period are Kukkiwon certified and practicing the Taeguek poomsae. So the pioneer's methodology worked, at least here.
Now there are people moving from other places and bringing their unique perspective into the mix. One guy, an ITF offshoot practitioner, calls his school "Traditional Taekwon-Do". His school is right down the road from my house. They wear cross over uniforms and practice non-contact sparring with face punching allowed and also do the Chang Hon forms. He showed up to our state championships recently and his comment was "How come the coaches aren't wearing uniforms?"
I think the probability of bringing him into the fold is extremely low.