Unless you are staying in the one place, few people would book five weeks of accommodation in advance, especially young people. When I was a backpacker, my plans would change depending on whoever you met along the way.
America seems to treat people they refuse entry to more harshly than most countries. Numerous reports where people are handcuffed and thrown in a cell, sometimes for days on end. Just refuse them entry and put them on the next suitable flight out if you doubt they are genuine tourists. No need to be heavy-handed.
The first time I arrived in the US at LaGuardia, the immigration officer was disbelieving when I said I would buy a car and spend months traveling around the US. I had the correct visa and a stash of traveler's checks, but it still took a ten minute interview before I was stamped in.
Even a long time ago, they kept pretty good records. A few months later, crossing the border from New Brunswick to Maine, I was pulled aside for more questioning. Back when I first arrived, I had put down my cousin in LA as a US contact. When later asked if I knew anyone in the US, I forgot to mention my cousin, as I hadn't actually seen him for years. The second officer looked up from his computer and said, "What about your cousin in LA?" Luckily they let me in again eventually.
Right now I would not risk entering the US (for various reasons). Some friends who have been on a few skiing trips to the US have said, not in the next four years. Japan or Canada will have to do.