Office chairs have a reclining mechanism. If you ever leaned back too far in an old office chair with four wheels, you would find out the hard way that four isn't enough. It's very easy to lean back comfortably and not realize you've reached the tipping point, fall back and hit your head on the floor or have a close call.
My first jobs long ago had four-wheeled office chairs, so you can guess how I found this out.
The fifth wheel goes a long way to preventing this danger.
You're much less likely to be leaning back in a regular four-legged chair so the front legs come off the ground, and if you do you'll probably be more aware that you are doing something outside the chair's normal mode of use.
And even if offices go out of style, office chairs will likely be around long past then.