What shrewdness? If the admirals were truly as weak as you seem to think, there’s little logical reason for teach to not have simply killed both Akainu and Kuzan and taken their fruits. Especially Kuzan who was no longer affiliated with the WG- no negative repercussions. Better to have a fruit that he can feed to someone he can control rather than try to strike a deal with someone he doesn’t, and can’t trust.