First of all, welcome to the forum. Thanks for posting this risk hazard at your own expense. Glad you were not injured more than you were.
With every box set up I've had over the years, I've always checked their balance. I start by pulling the first top drawers all the way out. Then with a slow smooth motion, I work my way down. I keep one hand towards at the top of the box feeling for any motion forward. Once I do, i start pushing drawers back in. Then I make a mental note. I'm not in the habit of opening more than one drawer at a time unless they are side by side. My latest set up is help together by a 3/4" plywood top with the boxes back to back. I plowed out a little depth on the bottom of my SO box side. The top pan depth is a little deeper on my Matco box. I cut grooves in the rest of the bottom of the top to lock them together. This set up allows me to open all 24 drawers at once with no signs of tipping. Not something recommended because a caster could get overloaded and push through one of the boxes floor. I also made a toe kick to go around the boxes. This keeps objects form going under the boxes when dropped. the bottom supports between the wheels are cut on 45's to keep the boxes locked in place from side to side movement.
It only takes a minute or two to remove the top, toe kick, and mat to move them around if need be.
File cabinets are a whole different matter. It's not that office people are dumb, it's a physics thing. Most lateral files are only 18" or 20" deep. Common widths are 30", 36", and 42". They can get pretty tall in 5 drawer form. Their drawers tend to be deep around 12". Opening the top drawer on a 42"x18" 5 high loaded fully with paper is a lot of unbalanced weight. If the bottom drawers are loaded lightly, it's worse yet. Tool boxes tend to have shallower drawers especially up higher. Most modern tool boxes have some sort of latching system to help avoid drawers opening by accident. File cabinet interlocks have been mandated by law since the mid 80's. In addition to interlocks, file cabinets can also have counter balances. You'll usually find these at the back and low of the cabinet. They can be made of steel (usually older), cement, and even composite nowadays.