I've been in that situation before, for several months. There is nothing cool about being homeless. You might get a sense of being "free", but the engagement is not worth the payoff(hope I'm wording that properly). A week or two is not the end of the world, but prolonged homelessness is when you realize how much you actually take for granted with the modern appliances like running clean water from your tap or a hot shower so you don't smell, toilet, washing machine, food being available few steps away. You need to work harder to maintain your life which means you start to sweat, that means you need a shower even more often than usual. Traveling away from the city into the forest to set up tent, wake up in the morning, put the tent into backpack again, over and over every single day, for months. When you need to visit the store, then you need to leave your big backpack outside, but where are you supposed to put it so no one steals it? And then you have to remember you need to carry all the heavy camping gear in your backpack on a regular basis while you're awake every time you're on the move. If you are ever on the edge of becoming homeless, try moving into your car, it is so much better protection from the outside, than a tent.
Btw, the rape statistics are exaggerated. It's still more risky for women in general, but most people who become homeless will NOT TELL other people that they are homeless, because it's shameful as it is. And people judge you very easily. A person does not have "homeless" written on their forehead as soon as they lose their house. If you're on the streets begging for money and set up tent there, then yes it's much more scary for women in that situation. But if you just have the same clothes on like anybody else and you walk around like you would if you had an apartment to come to, then the risk is not as big of being attacked by a rapist. Again, the homeless people you see at the side of the road with their tent up is less than 10% of all homeless people out there. The majority of the masses have an extremely narrow perspective on this issue and think that 90% are drug addicts or alcoholics and set up tents on the sidewalk or parks. That's not the case.