Perhaps we don’t see the Council much, or at all. We can hear about it and the dictates it hands down and see how various Jedi react.
In some religions there are cloistered orders (like nuns who live in convents and monks who live in monasteries) and there are those who choose to live non-cloistered lives (a nun can live on her own like any other person, except she’s a nun). Yoda could be the head of his [monastery]. And we could see various other Jedi without specifying how they live. The Jedi [pope]/Council could be constitute an adversary, many Jedi feeling compelled to follow what the Council says even if they disagree and we can see the disagreements and see what Jedis rebel.