They do sway, and I can see where side-braces would make it tough.
You might be smart to bolt them down tight, in case someone bumps into the rack hard.
By the way, just in case SOMEone might ever be as dumb as I was, don't do the following:
I stood a 4' shop fixture on its end, on the floor, so it would shine "sideways" onto the bottom four feet of some plants.
Then I was about to go on a trip, and watered more heavily than usual.
Water flows down.
Some water flowed onto the floor (where I was smart enough to protect the floor from water, but NOT smart enough to protect the 120 Volt lighting fixture from water.
Fortunately, I smelled "something funny" just before I rolled my suitcase out the door.
It wasn't actually very funny at all, and would probably have burned the house down if I had been 30 seconds faster.
P.S. That's how the British Columbia police said they used to catch hippies growing pot indoors. "We catch them when they burn their house down".