I disagree that it would be a mistake. Having said that provided that the ability exists to boot his ass if he so much as thinks of stepping out of line he could be allowed to sit as chairman.
But if he makes one wrong move they would have to bust his ass immediately so that everyone knew they meant business.
Such a thing would NEVER happen in the Good old Boys Club called the Senate.
They pride themselves of their colleagiality over their patriotism etc.
yeaaaaach.