Teach’s pitch to Kuzan was literally that Kuzan doesn’t have to follow his orders… he says that the crew can have their own separate agendas
Teach never gave a single order about “capturing Garp”… Kuzan simply fought Garp because it follows whatever agenda Kuzan has… and when Kuzan’s agenda stops matching Teach’s, he’ll fuck off and do what he wants
if Teach kills Kuzan, fine… the outcome is the same, Kuzan can’t reliably be counted as a member of “prime Blackbeard pirates”