That is quite meta..

But the recycling of souls is something I never truly understood. I do believe that Shinigami and Menos don't join the cycle. Those two seem to me like polar extremes of the spectrum, so Shinigami living mulitple lives is out of the question. The Cycle has only spoken of Pluses and Hollows. So when a Plus goes to SS, and happens to attain Shinigami powers, it leaves the cycle. Same with Menos.
I really don't see how Isshin differs, but that's partially due to my ardent dislike for him.
I don't think Ichigo
has those abilities, as you may have said. Example: his attack against Kenpachi. It wasn't something he was well and truly conscious of, something he could up and do whenever he wished it. Remember "resolve"?: which he used against Renji. I'm certain the only other time was against his Hollow to get Vaizard abilities although that wasn't blatantly clear.
I think that is what Aizen meant by His Words on the hougyoku. ( I just haven't understood: why Ichigo)
But about Yamamoto. His power may not necessarily come from seeking it. It is more likely to have been from constant battle. Apparently he has been in quite a few which is evident on his body.
One principle that has been forgotten in Bleach, because it was stated so long ago, is the one about a soul increasing its power when in danger of termination. We can attribute Kenpachi's apparently limitless powers to this principle. It is highly doubtful that Kenpachi went through the Academy but we do know that all he did before he entered Soul Society was kill people.
While people like Byakuya, Gin, Aizen were simply
born with high levels of power.
Ichigo's deal is simply because he's a hybrid. The wall between Shingami and Human was broken, and subsequently that between the Human and Hollow.