"if a team runs itself for six months while you search for a manager, you don't need to look outside, you need to promote from within"
Well, yes...
..."But I don't want to be a manager"...
..."But I've seen too many teams ruined by promoting a competent worker to a management role they didn't want, or couldn't do properly"...
Again, yes... It's a well understood phenomenon, called "The Peter Principle"; commonly stated as:
"In any organization, an employee will be promoted to their level of incompetence"
It's one of the biggest problems in organizational management...
...(And you should definitely read the book by the way)...
Which is why when you're faced with a situation as presented above, you need to do one of two things:
1. Flatten the hierarchy... remove the level of management in question as unnecessary and counterproductive... Assign administrative and project management support to the team so they can focus on what they're good at, and have the higher level management take on the remaining responsibilities the previous layer of management that are actually not just necessary, but critical. Specifically,
A. setting missions and goals for the team, in alignment with the organizations missions and goals, and effectively iterate and adjust them to optimize performance
B. Obtaining and distributing the resources necessary for the team to accomplish their tasks, goals, and missions
C. Advocating for and representing the team within the rest of the organization
D. Most importantly other than point A... manage and improve both the professional development, and the morale of the team members individually, and the team as a whole
2. If flattening the hierarchy won't work, for whatever reason, then find someone internally who has the aptitude and desire and is trainable to manage others, and then ACTUALLY DEVELOP their leadership and management skills and abilities.
The reasons managers get paid more... Or at least it SHOULD be and is intended to be... because their skills, abilities, aptitudes etc... are more rare than those with purely functional or technical skills; and even more rare than that, because they willingly accept responsibility for the actions, and the development, of others.
That second part is the big hangup... lots of great functional, operational, or technical people, either don't want, or honestly cant, accept that responsibility over others, and still be functional at the level they need to be. They don't want the risk and stress, or their core character causes it to be TOO MUCH risk and stress for them to be able to handle, without it hurting or harming them.
Please not, that doesn't make someone who wants the responsibility superior, or someone who can't handle that responsibility inferior... Just different, and not suitable for management or leadership.
But, so long as someone has the constitution, and innate character elements necessary, at the very least the skills of both management and leadership can be trained, and gained, and improved with experience; making for a competent and functional manager, even if they don't have a particular talent or aptitude for it.
... It takes natural talent and aptitude, as well as the various necessary character elements, AND all of the support and training and development, and resources; to become a good or great manager or leader... Or anything more than functional and competent... And importantly, to became any kind of actual leader, not just a manager.
To do that, they need professional development, and support from higher management and leadership; and they need to have realistic expectations set, with appropriate missions and goals and metrics, and the resources necessary to achieve them.
The problem, is that so often, none of that actually happens.