I guess technically as long as your within all your ratings than you are OK assuming everything functions properly. I towed a 20' loaded @ about 9K daily for years with a 5.4L. Most rigs have enough power to move you around. No you do not need a 600hp diesel to tow mowers. Actually you really do not need that for anything. Those are a luxury. A nice 250HP with proper gears will get you anywhere you need to go.
The thing is even though pickups are rated to tow these weights they are not designed to do it all day, every day. Doing it is possible, but you will rip up tires, brakes, suspension, ball joints, trannies, and overall the truck will require additional maintenance. My big thing is safety though. I spent too many hours back in the day keeping my rig legal, but every day I see guys with mismatched tires, no working lights, presumably no brakes, and fenders smashed to #%$&, all while driving through town like a sport compact car. We've since upgraded to proper tow rigs, but it concerns me that my family is driving around on the same roads as the guys with 1500lb mowers bouncing around and blowers dangling off the side of the trailer, or in this case a loaded 10K enclosed with no brakes.