In 2004 I bought a new F250 with the 6.0 diesel. 14 years and 117,000 miles later and I am still towing my 31' Airstream. Been almost coast to coast with it. Hauled lots of mulch, gravel, and dirt as well when not towing.
Had problems with the EGR valve and EGR cooler so I had the EGR delete kit installed several years ago. The wet bath oil cooler started leaking at 100,000 miles, which I understand is the lifespan of that unit. Had to replace the original alternator a few months ago. Seems to be having problems with the factory glow plugs or their wiring harnesses and I will have that checked soon before it gets cold. I plan to drive this truck for another 14 years and maybe longer.
If you find a 6.0 that is still running, chances are its had some of the known problems occur and was likely repaired. If you can find one that has some documentation of what work might have been done over the years, or maybe a one-owner truck and that person is willing to tell all, buy it.
When life gives you lemons, don't make lemonade. Go get the oranges that you really want.