For short, small (no. of persons is limited by space), stocky platforms around machinery may be got away without braces,...
Please do not pick and chose my words. Read the whole sentence. With the conditions have been met, the welds and brackets further stabilize the platform that render the braces un-necessary.
A four leg platform essentially acting as a vertical cantilever with load (platform floor & workers) on tip if the top framing and the columns are simply connected. Once it is excited, it vibrates and the tip moves, the amplitude of the movement depends on the mode. A (diagonal) brace from lower ground to the tip will diminish the magnitude of the movement, but not the vibration, which would still be felt if it is in higher mode. However, human are not so afraid of the vibration without associated lateral displacement.
My previous conclusion, as it still stands now:
(analysis on human induced vibration), which most designer chose to get away with by simply provide bracings, since it (interactive vibration)involves difficult & tedious analysis.