You're missing the point. The whole point of the alliance was to strengthen themselves against the unknown power that WH/Marines possesses.
While Pirates do betray each other, betraying each other in this crucial juncture doesn't help either of them. Similarly, Kaido dying or Linlin dying doesn't help the other side either.
That being said, Rocks Pirates were more or less self-destructive. Hence, it is doubtful that they can comprehend the situation sufficiently enough to properly work together.
In another words, neither Kaido nor Linlin wants the other to die till clear advantage presents itself. But that doesn't mean one will help out the other.