At 3, as you know, he has no understanding of the concept of death or serious injury. It is common for kids this age to think of themselves as super heroes. It is pretend for them, tho. I think that on some level they are aware that they aren't really able to do fantastic things. I think that you said the right thing when you said "wow, wouldn't that be cool, etc." When he talks about being a super hero I'd focus on the imagination part first and not try to talk about safety. Do say, firmly, after the imagination sharing "you are not to go into the street unless I'm holding your hand."
He's excited about being a super hero and not interested in safety when this happens. Go with the imagination and deal with safety at other times.
Your son wants to be safe and have the security of knowing that you will keep him safe. He will test the boundary of staying on the side walk. I suggest that when he runs into the street without you that you have an immediate consequence for him. Perhaps go back into the house, school, store or away from the street until he agrees to hold your hand and then hold it all the way to, across, and after crossing the street. Tell him you will have to always hold his hand until you can trust him to stay out of the street. This worked with my grandchildren. We had to do this several times, tho.
Same for riding his bike. Start out on side streets with little or no traffic. First time he rides into the street, it's back home with the bike, and then set out without the bike or he walks the bike.
My 9yo granddaughter is just now learning to ride her 2 wheeler on the sidewalks. I know that anxious feeling. She wants to stay on the sidewalk but does lose control and veers into the street. We stay on side streets.
I think it's possible that by summer you will have succeeded in teaching him to follow the safety rules.