This is certainly a red flag for the organization (not necessarily the whole company).
I have a very senior position in a very large company. I still like to be be in the hiring process of some members of my teams - mostly because I do not want to miss good candidates that may be a bit unusual.
When hiring for my first line, I always wonder if the candidate could replace me. It is surprisingly difficult to find such people, who would be hardcore geeks and want to lead others.
I asked the "would tout like to be in my position" a few times to successful team members. A few responded "sure". I had them present to the board, lead teams, and all but one came back to say that they are done and want to come back to what they were doing. The one that stayed did well, she is a good CTO today.
I can't stand people who are scared by others and would sabotage a team. I can understand that one is afraid of competition but in a sane and big enough organization this can be worked out.