I'm not telling you not to do it. I'm offering you legitimate advice. Most of the users on this site are offering you legitimate advice. You chose to ignore it. You are convinced of yourself.
You all just need to look outside the box. I can but I'm not sure if you can.
But you are young. And you've never lived on the streets, and you don't know what it's like. You have an idealistic vision of what it's going to be like to be free. How are you going to travel with no money? What are you going to eat when you travel? Soup kitchens are only open certain days at certain times. You cannot sustain yourself from them. And if you're travelling (again, how?) you're not going to be near soup kitchens all the time anyway.
No offense, but you are not thinking outside the box.
Homeless people showering at the beach, or at community swimming pools, is not an original idea. Not sure how you get the soap you mentioned. I guess you could rely on the charity of other people, like with the soup kitchen. Beg people for a bar of soap every couple of weeks. People who work might be generous and give you some of their pay. Somebody has to pay for it: for the soup, the soap, the water, petrol. Rather than you working, you'll just be relying on someone else working for you. Nothing comes for free. Animals work. If you want to have basic luxuries like hot food, soap and the ability to travel - someone has to pay for it.
You want your cake and you want to eat it to. And the world is sympathetic enough to support you meagerly. Even still, I think you'll find living on the streets to be a living hell. You sound naive and idealistic. From what you've said, I give you about a week before you return home with your tail between your legs.
YOU DON'T NEED TO FAIL.
Be open minded. Listen to the people on this website.
If you don't want to get a job, here's another idea. (I realize it's a bit dodgy.) Sign up for university. Take out a student loan for a couple of grand. Drop out of university and get a refund. Buy a plane ticket with the loan money. Leave the country. Go somewhere where being homeless means being a backpacker, not somewhere where it means starving or being stabbed and raped.
If you decide to return, you'll have to pay off the loan and the interest, obviously. It's not a fool-proof plan, but it does provide you instantly with the means to leave
properly and have a real journey.