Back in the '80s I towed a 13' egg trailer 2000 miles with a Dodge Omni. :D. I would tow with an Xterra ( if I could get past the stiff ride), as long as the TT was sized appropriately.
But yeah, some forum members would sniff and turn up their noses at the idea.
That CL16BHB has bunks. It could work.
Any trailer you seriosly consider, take a half hour or more inside without the salesman. Sit in it, lie on the bed, imagine what would go in which cupboard or drawer. Think whether You would be ok sitting inside it all day in bad weather.
You have the right idea. No better way to see the country and experience the great outdoors.