So technically the answer is yes: hanging is a valid installation method for some base cabinets (I've installed Ikea kitchen cabinets that way). But I agree that hanging them at head level is a bad idea for all the reasons PPs mentioned.

They are generally much deeper than wall cabinets, too.

You wouldn't be able to reach into the back without standing on a chair or a ladder. Base cabinets also don't typically come with a top because they are expected to be covered with a countertop and most styles have a drawer over the cabinet.

They aren't built to hang, they would look weird and stick out too far.

Lol no

New homeowner here. Can a base cabinet be hung on the wall in my laundry room? The base cabinets have more space than wall cabinets.