Michael, both cool-headed and ruthless, did not need a counter-veiling force like Tom. Also, Vito may not have anticipated how threatened his Family would become. Tom was not suited for such a death struggle, as was clear to Michael and Vito.
I think towards the end of Part II, Tom was also pretty expandable for Mike. They really could have made something of this in Part III. It's a shame that Duvall was absent, I can't say this enough.
"It was between the brothers Kay -- I had nothing to do with it."