Car free on the day with the least transit service and what little there is randomly gets delayed or cancelled without notice. Great idea!
Seriously, as someone who exclusively uses transit, the weekend service is infuriating and basically unusable if you're under any sort of time pressure. You show up at a bus station, transit app says the next one is in 30 minutes when it would be 5-10 minutes on weekdays. So you resign yourself to a 30 minute wait only for the bus to not show up with zero announcements, even though they're pretty good at notifying you of these things on weekdays. So now you have to wait for the next one in an hour, which might not show up either, and when it does, it's packed to the brim because it's carrying three buses worth of passengers and the driver puts on the "sorry bus full" sign and refuses to let you on even when several people get off at the same stop. It's genuinely like they want you to drive on the weekend.
Calling it now: when car free Sundays inevitably flop because no one wants to bother with the shitty weekend transit, city council will go "see? car free streets never work!" And it will be used to shoot down every subsequent car free initiative.