Keith yes black holes will eat dark matter but there does not seem to be halos of dark matter surrounding black holes. We can't see it. We do assume huge amounts of neutrinos escape. There is gamma ray evidence from Andromeda that its central black hole is eating something.
We do not know if dark matter gravity is in fact equal to baryonic gravity or not. The only evidence we have of dark matter is gravitational lensing observations and cohesive galactic disc rotation. So we make assumptions.

For myself a good place to start is 'where does/could dark matter come from'.
Some think it came almost immediately after the big bang. THE BIG BANG IS JUST AN ENTROPY EVENT where a highly energetic whole goes to a lower energy state and spreads out, I claim it came much later.
Those who think it came into being quickly before inflation think dark matter is like smithereens of microscopic pieces of black hole density particles. (but they don't interact and grow?)

*I claim dark matter came from the annihilation of baryonic matter charge and spin with opposite anti matter at a ratio of a billion anti matter particles to a billion and one positive matter. This could be how normal matter got an advantage and why we see a universe of normal matter. Everything else turned into energy and the new residue of annihilation energy that reconverts to matter and we now call dark matter.

WHAT IF there were unannihilated anti matter pockets that repelled collision. It might be the pockets of empty space that are usually 20 light years across that has an anti gravity and is acting like the repelling dark energy, as space expands, the larger regions of anti matter continues to repel more like an accelerated push.

(you would think something would have set off an antimatter explosion by now in these seeming empty regions.)

A third assumption about dark matter is that it does not exit. Instead gravity is not a fundamental force but is an emergent force like temperature comes from friction. a trick of gravity propagates what seems like dark matter, -Van Der Linde theory

Your best question is why would the rate of BH creation increase?
must wait = its a doozy.