Standing in place is actually way harder for your body. The muscles in your lower back are always tense when you stand. Whereas when walking, they get relaxed and then tense up again. Imagine doing 20 push-ups in 5 minutes. Now imagine doing 1 push-up in 5 minutes (staying low)
Standing still causes all of the pressure to be applied to the same region and the same structures, same goes for muscle activity. When standing still we tend to search for energy conservation and our muscles stop being active, transferring all of the pressure/stress to the passive structures such as ligaments, joint capsules, intervertebral discs, etc.
Gait is a complex system of different muscles that continuously work in sequence, therefor we stay active and we don’t transfer the load to our passive structures and we continuously shift the load to different places.
Standing requires constant contraction of musculature that is required to keep us upright whereas walking is an innately efficient means of movement that stores potential energy and releasing kinetic energy with every step
Additionally standing still keeps constant pressure on our spines which does not allow synovial fluid (the joints lubrication) to flow as freely. It also hinders the pizioelectric effect of our spinal discs (think fluid moving in and out). This is why we say motion is lotion!
67.5% of your bodyweight rests upon your lower back at all times. (Head, 2 upper limbs, torso) Which means that your lumbar discs are compressed more than the thoracal and cervical.
When standing still, you’d see your center of gravity constantly changing in a really (really really) small area. This is because you’re constantly (subconsiously) adjusting it.
You’re basically swaying back, forth, left and right the entire time.
That’s where we factor in your muscles (core: abdominal, lower back and lower pelvic muscles), ligaments, tendons, spine, discs that make sure you keep that certain position. This is mandatory for a certain degree of static stability.
However, when we move, although everything above is also working, we have our momentum and other muscles compensating and working in couples to maintain our dynamic balance. The load is more spread out.