I got stuck once on wet grass when pulling my Airstream with a rear wheel drive truck. So my opinion is yes, 4x4 is needed if I leave the pavement while towing. But many people use 4x2 and are happy with it.
With any half ton truck there is an issue with payload if one hauls gear in the truck bed while towing. That 4,100 lb rear axle rating with the max trailering package helps. I've had two tow vehicles with the max trailer package.
I have the same issue with fishing rods as you. I need a suggestion also. So far I have carried them inside the bed cap. My 10' surf rods don't fit anywhere without taking them apart. When I went trout fishing in the mountains a few weeks ago, I arrived with a broken rod tip on my 6', with no apparent reason for the break. I'm thinking of adding a rack inside the cap.
I have a ARE cap with factory installed Yakima rails. I carry my 15' canoe on top of the bed cap.
2014 Silverado 1500 Crew Cab 5.3L maximum trailering package (yes, I'm towing the 34')