If they had alcohol and prostitution inside the cars they could increase the ride length. Or something... I think that came out sounding wrong.

They imply that looking at crime data reduces average wait time, but they don't actually present any data to show that this is the case, or to quantify how much better their demand prediction model can do when given access to the crime data.

That would require a 'before' and 'after' with some numbers that prove that they've managed to decrease the wait time in a statistically significant manner.

Agreed, there could be more direct evidence. They are assuming that this correlation will hold true in most cities.

Perhaps a less contested statement would be: "How Uber makes prostitution and alcohol better"...