Kaido has to show his awakened form as, unlike Big Mom, his role in the story should be over after Wano. Very doubtful that Blackbeard takes Kaido's fruit. What would be the point? Up his threat level? If that's the case, the best thing that could happen is him acquiring an ancient weapon.
How do you know he hasn’t shown his awakening, he has to announce it?. And no I don’t think he has to show it, he has shown to be OP already and so has Big Mom. Did Whitebeard show his awakening?. We don’t know, he probably did. The thing is that he showed that he was op just like the other 2 emperors.
On Blackbeard third fruit, that’s his thing, trying to get stronger which he would with Kaido’s or another third fruit, so yes there’s a big point to it, besides everybody has theorized that he will get a third fruit.