If you look at the internet you will see an enormous amount of information about desk stability and a lot of it is wrong.
So we would advise to largely ignore it. Standing at the end of a desk and pushing it is not a good representation of how you will use the desk nor its stability. This tests the response of the desk to forced oscillation setting up essentially simple harmonic motion.
Low amplitude non-forced oscillation is the main concern for standing desks as you either type on them or write on them. Let's face it keyboard typing is the most prevalent use case and how well this is handled by the desk is what is most important to users, We design our desks using computer aided design, analysis and manufacturing to ensure the desk is stable and is well damped. We try to balance the desk weight against it's rigidity and we use finite element analysis to focus on each aspect of the design.
In the end the desk does have to move and the leg sections have to slide one inside the other. Basic geometry means even a small movement at floor level equates to a larger movement at desk working height. So at top height (1.3m) the desk will not be quite as stable as it is at say 0.7m. Could we make them more stable - yes - but not for the same price, with the same aesthetic design and at roughly the same weight and definitely not the same cost. Desk design is a compromise between many factors.
In practical terms, what does this mean? Well, our Series 2 square leg is the most stable desk we have ever sold or tested due to the aspect ratio of the legs. The Pro version performs identically to the standard version in terms of stability.
Looking at the historical data, having sold thousands of desks (and some to customers with a real concern on stability) we have never had one returned. As long as the desks are built correctly and loaded to a reasonable weight we can say that in almost all cases clients are very satisfied with the stability. Note a stable, solid, level floor will greatly help stability. Any desk foot movement is undesirable.