Our German friends let us borrow their son's bike after he got too big for it. I guess it will still be called a "bike" because it has two wheels.
See. No pedals. We don't need no stinkin pedals. Really, this is a great way for kids to learn how to ride. They just start off kind of walking while sitting on it. As they go faster, they kind of get the hang of how to not fall over. As I have said before, this is counter intuitive - if you are falling to the right, turn to the right.
I don't know if you can get a bike like this in the U.S., maybe you just need to find a German friend. If you want to read my older post about learning to ride a bike and why training wheels are stupid, check out my post on bike riding
Maybe the issue is an economic one, rather than a cultural one. While a bike without pedals may be good for starting out on, kids with one of those will quickly develop the ability to stabilize one, and then want one with pedals. But, rather than scrapping the pedalless bike, maybe what's needed is a pedal bike that has a crank that can be removed?
They aren't cheap but are available in the US from:
Just Google 'balance bike'
Amazon.com alone has > a dozen varieties, some at around $100