Speaking as a guy who has towed quite a bit while carefully paying attention to the limits, I would say that the Leaf is pretty much the last vehicle I would select for that purpose. I've towed a pop-up camper with my 2001 Forester (manual stick) through the Rockies, and similarly with a little Mazda mini-van. But always while paying attention to proper setup and vehicle design limits.
No, I don't believe the only safe vehicle for towing is a giant truck. For the record. But that doesn't mean just any vehicle will do either. Range will be a real issue, for example, even with the bigger battery.
We have a small travel trailer now, single-axle, GVWR 3700 pounds, with a 400 pound tongue weight. And yes, we own a hydraulic scale, so that I'm not guessing as to the actual tongue weight. We tow that camper through the Rockies with our 2015 Q5, rated to 5000 pounds on grades up to 12% and 4400 pounds on any grade (30% is the vehicle limit towing or not). Actual trailer weight when towing is about 2950 pounds, give or take.
Front wheel drive in general is not your first choice for a towing application, for starters (and yes, our mini-van was front-wheel drive, and we stayed well-inside it's towing limits for that reason). Proper set up is critical to keep enough weight on all the wheels for braking and turning purposes.
Tongue weight matters for other reasons too - at least 10% of the trailer weight on the tongue, or you're asking for serious sway, which can be really dangerous. I seriously doubt that the Leaf is able to handle enough tongue weight to be able to safely tow any significant load.
So no, I don't think it's simply a matter of Nissan not wanting to spend the money to test and certify. You're well outside the design parameters of this car if you want to tow anything more significant than a tiny trailer with a small rented piece of yard equipment of something of that nature - hundreds of pounds, not thousands.
Wrong tool for the job. You can drive nails with a screwdriver if you're really wanting to, but it's a heck of lot easier with a proper hammer.
Just because some people do something doesn't mean it's a good idea. Can you get away with it for short distances? Probably. But if you do need to do any kind of emergency avoidance, I don't want to be anywhere near you on the road. Ditto you descending any kind of lengthy grade in heavy rain while negotiating corners.
Could you? Probably. Good idea? Should you? Ummm, no. It's unwise.
My 14 cents.
Edit: I watched your video - missed that link the first time through. Very cool little camper! But 750kg is the empty weight, not your towing weight. What I wrote above stands. It's quite tall - I think you'll be surprised how fast your range goes away.
Here's a video that explains the physics involved in a digestible manner: