i'd argue that nearly all drivers who failed massachusetts's background check would likely provide very similar quality rides as current uber/lyft drivers. the utility to all of those now-working people certainly wouldn't be outweighed by the disutility of a potentially small (and probably statistically insignificant) rise in bad rides.
people make mistakes, but people change constantly. we should encourage positive change in people, not discourage it. allow people to do legitimate work despite past mistakes, rather than compounding the punitive effects of their mistakes and thus encouraging more bad behavior (often out of despair or desperation).
uber has made many mistakes, but i agree with them here. let these people work.
by contrast, uber & lyft are able to do background checks with less than a ~2% adverse action rate.
it's debatable that background checks make passengers safer, so getting rid of background checks altogether would be the most efficient of course.
checkr (https://checkr.com/) has built a nice little business doing background checks despite the inefficiencies.