Just like kung fu, the true foot movement has been almost lost. In studying Yang tai chi, along with many years in kung fu, I respectfully attest that tai ji does have proper footwork if taught. However, the up and down movements described, unless I misinterpret the comments, are contrary to rooting, expressing chi, and using fa jing with silk reeling to express out through the hands. What seems to be missing in this conversation, from my perspective, is the connectivity from feet to waist to shoulder, expressed through the sunken elbows through the hands in a whipping, penetrating, and/or soft to hard notion (steel wrapped in cotton concept). While ba gua has obviously great circular and 8 step movements and hsing-i is very expressive in its stepping and hand jing, other than chen is more subtle but just as effective. I personally consider Chen style the bridge historically between external kung fu and the taiji expression (this is my concept only!). The Yang style has, at first, what appears to be very stagnant footwork and little expressed jing. However, and maybe my tai chi sifu, Jeff Bolt, and his teacher, Dr. Yang Jwing Ming, taught us differently, but we were always shown tai ji chin na and moving applications through the use of movement and proper footwork. The standing push hands were a beginner's trip until sufficient enough in relaxing, bridging, and sticking, to begin moving. We had many drills for moving push hands, and sitting in our root for that instant, and jinging to our opponent through our push hands sensitivity. It also helped me that I also had my kung fu to understand foot movement and application as well. In fact, without foot movement, all Chinese martial arts is stagnant and ineffective. A gross example: look at traditional wing chun versus modified and how different that is in relation to footwork. Of course, in a real fight, everything evolves and changes, so to not practice footwork is inpractical. If you can find the book, Yang Tai chi Transmissions, by Yang Chen Fu, he describes the footwork well in poetry form! And, he was a very large 300 pound man who could root and glide easily.
A last point: like the external, tai ji could not have lasted this long and be called "grand ultimate boxing" if it was grossly ineffective in fighting. Like everything in nature, only the strongest fighting methodologies and species survive. This was used in warfare alongside the external arts and, in fact, I know few legit kung fu masters who also do not incorporate the footwork and connectivity of tai ji.
Just my humble observations and personal experience on tai ji footwork.