You can use your axe and hoe while controlling the cart, no need for a second player. I use the hoe to flatten ground in front of me as I go (seems to work better than path option). And I pull out my axe if I have to chop down a bush. I never have to stop moving forward to do this. For silver I just load it up and push it over the steepest edge I can find then go down to the bottom, rebuild cart and load it up again. Being able to bring back 100 silver or 100 iron in one trip is very beneficial and I have never had a problem using it that way. They are also great for early storage options before Iron. You can make a few stationary ones in or outside your base for better inventory management. Also less frustrating than the raft for me on short waterways. Just build one, push it in the water, jump in the back and as you run you will move through the water.

The weight definitely affects movement, I always have my personal inventory to max weight to not over burden the cart. Also, and maybe this is my imagination, but it seems the weight is distributed like it is in the cart inventory screen. SO if I put ALL the silver on one side it tends to lean/pull to that side. I try and evenly distribute the weight from left to right when loading it up. I have noticed this same mechanic on boats also with leaning.