This will vary on what Grip was saying. How fast are you traveling toward the wall? What is the wall made of? What are your shoes made of? How high do you place your foot? Is it wet out? All these things need to be considered to get the highest height.
So to answer your question "Is it possible to do without any traction whatsoever?". The answer is maybe. It depends on how high the wall is and the above considerations.
Let's say, an average speed, not sprinting, but a paced jog. You pointed out that I meant friction, you're right. But you have to take in consideration that
I'm talking about running up a glass/marble wall with socks.
There will be very, very little friction in my example. When I posted the topic, I wasn't asking how to get the highest height, but if it's even possible to perform under these circumstances. As a bonus, let's make the wall wet too. The wall will estimate to about 8-10 feet.
Running up a dreaded slick, flat, and soaked wall while wearing nothing on your feet but socks, is it even physically
possible to gain any more height than the initial leap to plant your foot onto the surface? Using perfect technique (which is probably unrealistic), using optimal foot placement, and normal speed and force, could I use the little frictional force available and go upwards, let alone reach the top of the wall?