I guess I always wondered why, if a Lord Commander Militant could rise/be selected from amongst other unaugmented Humans, a Chapter Master could not be either selected or voted in by something approaching a plurality of the Adeptus Astartes Chapters.
The requisite "respect structure" probably already kind of exists, if you think about it. It's implied in several novels that First Founding Chapters are accorded a great deal of respect, and that Second Founding Chapters like the Black Templars at least some times have feelings of superiority toward newer, "lesser" ones.
Given this, I doubt most Chapters would object if the High Lords of Terra were to vote in the First Founding Chapter Master that seems to most exemplify the virtues they require.
Personally, I think that when the Primarchs disappeared and the situation was such where no clear leader of the Astartes could arise (especially given the Codex Astartes), the High Lords were secretly relieved that they didn't have to share power with such superhuman zealots.