But dogs typically get it from the bat. I don't understand the logic
It's not that hard to understand.
Humans rarely get infected by bats.
Bat populations are large and not practically reachable, so vaccination is impractical. Eradication is undesired because they serve a useful niche in our ecology.
Dogs are the primary way humans get (got? with higher vaccination rates for dogs this has been skewed, like how the most common causes of death have changed as things like antibiotics were developed and various medical interventions for certain cancers and other conditions) infected. Dogs are typically socialized, so vaccination is practical. Dog populations are smaller and generally reachable. Feral dogs can still be a problem, but catch & release with vaccination and sterilization can reduce their population and risk factor over time (similar to what is done with cats).
So if you want the highest impact intervention, between dogs and bats the place to intervene is the dogs since you cannot, practically, intervene with bats (by vaccination or eradication).
I've been bitten or attacked by dogs multiple times. Can't say the same about bats. Maybe vampire bats but I have never visited their range.
Bats carry, but don't develop rabies so they don't usually attack dogs on their own - except for self defense, when they're attacked by a dog.
Rabid dogs are typically aggressive and spread the infection on their own.