I noticed the speed increase after each part, which is a great idea. When I had all the parts and the objective said to deliver pizza to the houses, I felt faster, but then I kept going in the wrong direction. I went to house 6 first, I think, but nothing happened. I assumed I needed to go to house 1 and count up. When I was looking for house 1, the movement became a problem. When I quit the game, I noticed you included an hint or maybe it was the objective that said I needed to go house 11 first. There were some areas of the road that were lighter than others, I thought it meant I could cross them, but there was an invisible wall.
You make a valid point about rules. The player needs to know what they can and can't do from a gameplay perspective and the world should be built around that. Personally, I don't think it takes away from the player to be able to cross the road. I'm a zombie pizza man now. If I get ran over again, I'll put myself back together again. It makes me feel less constrained to the world you created. I noticed your level design leads you to the next objective, but I'm a player that will always go left first when you tell me to go right. When I went the wrong way, it felt like more work to get back to where I was and find the right way to go. Maybe a pointer to the next objective or a map would help a player like me out.
Having invisible barriers is a great way to lead the character in cinematic experiences, which makes the first part of your game so strong. I think you can keep the invisible barriers, but there should be indications where I can cross like a pedestrian crossing sign. If I see that sign between both sides of the road, I know there is no invisible walls and I can proceed. I'm not sure if your game featured an area between roads you could walk on except for the beginning, but having a crosswalk you could cut through between roads would make it more forgiving for players to explore.
I think your game is probably the most memorable game I've played this jam for its beginning. It may be just the type of player I am, so take my critics and suggestions with a grain of salt.