"A car and a bike travelling at the same speed will cause vastly different amounts of harm on impacting the same object."

Theoretically, then the bike should be stopping. Two cars colliding at 15 mph is less dangerous than a bike hitting or being hit by a car at 15 mph. I doubt the stopping distances are that much different (probably 20 vs 30 feet).

"in that case the stop sign should just be a yield sign."

Well, most stop signs could just be yield signs. Looks like they're doing that for bikes. Would be nice if they do that for cars too.