The primary benefits of a camper of any sort are mostly intangibles. Like not getting a rash. Or bedbugs. Not having to pack and unpack all your clothes. Having your OWN bed every night. Being able to cook your own meals if you are of a mind to do so. Being able to take along your favorite contraband from the airways.
As for saving money, well, maybe. It really isn't all that clearcut. If you stick to WallyWorld parking lots with a few COE or NFS or BLM campgrounds (for $10-$20 a night) and cook ALL your own meals, then yes, you can save money. If your tastes run to fancy camping resorts at $100 a night, then probably not. YMMV.
Tell your friend "different strokes for different folks" and "don't buy a camper/motorhome" and "have a great time however you choose to travel.