Your approach is not terribly strong agianst the structure "collapsing." A diagonal is deisrable. The simplest might be an "X" of plumbers tape.
This said, your design and ~smontes's both have admirable traits. His, will shed a spill. ok. Your's, harder to clean, could contain one...! (His is outside; your's in inside...!) Your's could even have multi-level spill drains. A top most draining into a hose barb w/hose, could (if valved,) be washed and drained, or for a failure of a topmost container, drained below to the next level, to add capacity, and later drained, elsewhere.
Under kitchen sinks I often add linoleum and caulk the corners, & the sides 1" up. (If it runs onto the floor, you know there's a leak; instead of it runing under cabinets causing *serious* damage.) Similar effort makes these temporarily water-proof. Sinks, as it were.
I can see that a part of the structure, with sides & doors, or curtains, could be kept cleaner & used as storage. But if you have storage, having a 3-tier that collapses could be handy! Flatten and slide under your bed! (Orrrr... just hang on a wall... ;>) Add 2 large washers between wood at each carriage bolt, then use wing nuts. Remember the plumbers tape. Zinc is common & cheaper & stronger, but it's available in copper! ;>)
Trickier would be a rolling cabinet that has just a side that folds out. No harder, just all the figuring... the choices. SOO many choices! But less floorage and equipment, dust free. (In case yours gathers dust. ;>)
BillSF9c ('Frisco area)