We travel with our fresh water tank filled most of the time heading off from home. Having it full or empty tows better than 1/2 full as it can slosh around. Maybe not a huge issue, but I know some that disslike the feeling.
We also sometimes wait between weekends to dump as the 2 of us don't fill the black or grey tanks after a couple nights.
With that said, I do know 1 person that had their fresh water tank brackets break after going over some serious bumps. The tank fell onto the trailer axle and bent it. The trailer was still towable, but they required a new trailer axle and new tank brackets. The incident which caused the damage was not typical and also caused damage to the rear frame skid plates (those metal triangle things), but I do not know what places you're taking your trailer. This was not a Forest River Product.
The water tank straps may be small, BUT, the idea that the straps are not designed to carry the load while towing is not true. Other than GVWR concerns of the trailer and ratings of the TV, There is nothing in the user manual that I am aware or warranty coverage that suggests that you can not carry water while towing - in the fresh water, grey water, or black water tanks.
YMMV but to me the whole idea and purpose of an RV, whether it's a trailer to a Class A is to get out there and camp. You're not forced
to go to campgrounds with water and dump stations. You may need to take your water with you and bring your poo back. Just sayin'