Pedestrians and runners don't stop at stop signs and it doesn't seem like a problem, so it seems clear to me that "everyone is required to stop at stop signs all the time" is not the only workable legal solution here.

In Oregon we just passed a law that lets cyclists treat stop signs as yield signs. I ride a bike as my main form of transportation and additional visibility and low speed of bikes makes this a no-brainer--it's quite obvious whether cars or pedestrians are approaching as you approach a stop sign.