I've towed with and without my cover.
Advantages with cover:
You don't have to stow away everything, because nothing can get blown out.
The inside doesn't pick up a bunch of road dust, even when wet.
If it rains, you don't end up with nasty road grime that's difficult to clean off the cushions and rug.
Advantages without:
You don't have to take the cover on/off... which isn't much of an advantage, because I put on the cover after I've cleaned the boat anyway. And if I'm towing the boat before I've cleaned it, there's usually a bunch of wet stuff (towels, wakeboarding vests, etc.) in the boat, and it's easier to leave all that stuff in the boat and just cover the boat until I get it home to clean the stuff and the boat.
Regarding your bad back, have you seen this backsaver product? No more crawling around to position those stupid poles: