I've debated some way to carry one. When we first started full-timing, I carried it in the pickup bed in front of our hitch. Now there are totes full of other stuff there. We ultimately ended up leaving our tote with the camp host at one park we frequent since that was the only place we ended up staying for a longer period than we could go without emptying tanks (about a week).
When that tote wore out from being in the weather all the time (cracks, leaks, etc.), we recently bought a new one. I debated carrying it around again, but ended up putting it in our storage unit (near the same campground) when we are not in that area. Again, that campground is about the only place we ever use one, realistically. Also, since it is going in storage, I only run gray water through it and flush it out at the dump station.
With that said, if there were a simple and secure solution of storing it on the go like you are asking about, I might be inclined to do the same.