I'd suppose minimums are to prevent pinch flats. I'd also guess they are conservatively high, just like the max is conservatively low.

I recently set up a trailer that my wife got me, and it came with cheap plastic rims and nylon tires. The sidewalls say INFLATE TO 35 PSI. Exactly! There's no room for error! The negative Amazon reviews of the trailer all have to do with the tires blowing off.