Relative to CTs on bikes. Legality - you need to understand what the requirements of your particular location are. The UK has more stringent inspection requirements than the US. In the US, there is no legal issue against running a CT on a bike. As far as I understand, the DOT wording on a CT is the same as the DOT wording on a Moto tire. The ratings on the tire are for load, temperature and treadwear ratings, and the DOT info is date of manufacture.
Insurance - speak to your insurance representative personally and make your own informed decision. In the US, unless the accident is clearly a tire related issue, it's not going to be an issue. My Ins. Co. accident investigator simple said he looks at the tires to see if they are round and black and have tread. He has no concern about brand or suitability, that's simply not part of his job.
I've run into shops that would refuse to install a CT on a bike wheel, but there are ways around that. As to fit and function at the bead, I have had no issues with getting the CT bead to seal on a proper width wheel. As I have said, I'm not sold on running the CT on the narrow Super Ten wheel, as the size available in the US is rated for no smaller than 5.5", IIRC.
Your previous experience is somewhat dated. I suspect you were attempting to mount a tubeless radial tire on a moto wheel designed for a bias ply tube type tire. At least in the tires in modern radial sizes, the diameters are no different. CTs and Moto tires in tubeless designs have somewhat different bead shapes, but much of this has to do with the rim protection built into many modern CTs. The CT will fit the Moto wheel such that more rubber is outside the edge of the wheel, but the sealing area is right where it is supposed to be. Auto wheels have a longer lip on the rim, but this does not impact how the tire seats on the wheel or it's ability to stay on the wheel. In my personal experience mounting CTs on moto wheels, getting the second bead on takes some experience and technique, but it's not going to come off unless you are taking it off.
Like moto tires, CTs vary widely in feel and suitability. Choosing a CT with a more rounded edge profile makes the bike handle much better than a very square edge design. Many modern CTs are fairly square shaped to give better tread life.
Traction wise, the CT is far superior to any moto tire. More tread blocks means it handles wet and marginal conditions like sand on pavement much, much better than any moto tire. You never ride on the edge of the tire, a common misconception, and typically even at peg scraping levels of lean, you still have a third of the tread or more on the ground. There are some handling quirks of a CT. Transitions across edges or angles require a bit more attention and typically it takes more pressure on the bars to engage a turn, but once muscle memory is formed, this is not a conscious thing.
CTs are not a choice for most riders, and that's as it should be. But for many, it's a proven option. Finding a replacement CT in the middle of no where is far easier than finding a Moto tire. They last longer, and handle a wider variety of conditions better than moto tires that tend to be more specifically designed for road or trail, etc.
I now return you to your topic of best street oriented tires for the Super Tenere. I have 4500 miles on a set of PR-3 Trails and so far am impressed by how the rear is holding up to a lot of slab riding. It's showing some wear, but isn't squared off. That's an improvement over many other Sport/Touring tires I've run on other bikes.