So have you noticed on even the cheapest of manufactured stands, they’ll use some sort of sheathing on the stands? Even on the open sides, there’s usually a triangle attached to the corners. That’s to keep it from moving laterally. All your supports are for vertical strength. But if you pushed from one side, I would bet it would move. Even slightly. What happens is all the stress is placed on the screws. They will fail if this pressure is too great. I.e. someone leans on it, you slip on a ladder and put your hand on it to brace yourself, floor sags, foundation becomes unlevel slightly, etc.
I would at very least, put 90degree supports under the tank. That way it’s still hidden and open like it is now, but greatly strengthens the stand from being able to move side to side. Tying it to a wall does a very similar thing because your walls are tied to other walls, rafters, etc that make them not move. I’ll draw up a quick example.