I'm not sure I get what you're saying. The Shivans preserve by destroying the 'sinners', as the Ancients put it. They don't actively go out and nurture new species. The destroyers are destroyed, and all the species that said destroyers would have wiped out instead get to grow up and take their turn at judgment.
Which is a false dichotomy. They're still going to end up destroying what they preserved earlier at some point. It's still wasted effort.
In this theory, everybody gets a free ride up until the point where their attitude towards other species starts to matter - i.e. when they run into other species. The Shivans are a filter.
Which isn't as effective as prevention. If this is really their purpose and they're capable of rational evaluation of it, they ought to have realized this.
The first the Shivans probably notice of a species is when it starts using subspace travel. That's when it becomes a threat to create a galactic/intergalactic monoculture.
But they can do better than that. They can prevent threats totally rather than letting them emerge. It'd be easier, and it help prevent monoculture much more effectively by having greater diversity.
The Shivans don't need to evaluate all the nascent potentials on multiple worlds. They're not a terrestrial species. Suggesting that they intervene with pre-subspace cultures is like claiming we should extend our law enforcement to apes.
If the apes were eventually going to be our neighbors, that would make quite a bit of sense, wouldn't it? Uplift is a classic science-fiction concept. Even if you hold onto the concept of "pre-subspace noninterference", the Shivans could still be more proactive once a race discovers subspace. This "wait and see" approach ultimately limits diversity as I will note below.
In short, the most efficient way for the Shivans to promote diversity is to wait for new starfarers to present themselves, give them a while to see how they act, and then either ignore them or throw a test their way.
Aside from it being easier to influence rather than destroy utterly making a mockery of your argument, there is another issue. In destroying, they also limit diversity. If they preserved these species they would later destroy instead by giving them a nudge in the correct direction, or simply being there immediately to greet them at the end of their first jump and explain the facts of the universe ("Be nice and we won't wipe you out."), diversity would be
enhanced. There would be more species, more cultures. All evidence we have is that the Shivans are capable of rational thought, so they must know this.
You're right to assume the Shivans simply don't care. But that's because they're not caring about diversity at all. There are better approaches for preserving diversity no matter how you cast their interest or when it occurs or their conceptions of numbers (which I would warn you, you're making assumptions about).
They're not out there to preserve, not by design at least. Either they are incapable of rational evaulation of this drive, or it is not their driving purpose. Pick one.