A hamster needs to run to stay healthy and happy. I am wondering, if a hamster was given a large enclosure (like the size of a room that is 300-400 square feet / 28-37 square meters), would the hamster ever need a wheel to run in? It would seem that the hamster could just run around the room instead of ever needing a wheel.
Not advisable unless you make certain modifications
Hamster proofing an enclosure of this size is quite hard. Hamster can climb to beds, sofas, heavy curtains and any wooden furniture with 3-4 cm separation from any flat surface. It is especially dangerous to have heavy curtains in the room as hamsters are excellent upward climbers but they are very clumsy when it comes to climbing down. Also, you have to make sure that they cannot squirm under the door. This is very hard to ensure as they would chew away the foam under the doors.
Long story short, this would work only if the room is solely dedicated to the hamster's use.
Hamsters require enclosures as much as space
Hamsters are especially stressed if they cannot find a good enclosure to build their nest. So, a hamster would run in the room until it finds an enclosure. If he cannot find one, he would go to a corner and make it his own uncomfortable nest.
Also, while young hamsters are more adventurous, old hamsters prefer a well known closed space over a larger area that hasn't been explored. Whether your hamster is old or young, they have to have access to their nest with the familiar smell.
Hamsters might not know if they are running on a wheel
This is still a theory as cognitive abilities of pet hamsters are yet to be studied, but hamsters may not know if they are not getting to anywhere. I have two stories:
One of my Campbell hamsters picked up a fight with his cage-mate and just before things turned physical, he jumped on the flying saucer and started to run for his life. He kept checking if he is putting distance with his mate and whenever he saw his mate just behind him, on the ground not on the flying saucer, he tried running even faster.
I put hamsters in large balls on a stand when I clean their cage. They usually run in the same distance for some time, stop and assess their environment and then run in the other direction for a similar amount of time. This might be due to them feeling they are too far away from their origin and want to return back to it.
In other words, large enclosures are not a replacement for a wheel/ball/flying saucer. A hamster would be happiest in such a large dedicated room with access to their nest and their wheel.
My experience with kids hamsters running loose , is that they do not want to go back in a cage and make homes in furniture. etc. I had a pet squirrel many years ago and he made a nest on the top shelf of the pantry by shredding toilet paper stored there. That is another point ,the hamsters will shred stuff to make nests. And what they decide to shred may not be part of your plan.