It’s NOT illegal to visit Cuba for shits and giggles. It’s illegal to visit Cuba without proper permission, which for the average tourist that means going through an authorized tour agency. These are off the shelf package tours that anyone can sign up for- go to the website, enter your credit card, show up at the airport and BOOM you are now legally in Cuba. They don’t care if you are a distinguished cultural ambassador or just going out of idle curiosity. As long as you use an authorized channel, you are good.
These tours have a cultural focus, but that doesn’t seem mean much. They do things like go to musical performances, visit national parks, tour museums and shop at handicraft markets— more or less what a visitor to a developing country would do anyway.
Here is the OP:
I’m not sure how you read “I am only and exclusively interested in an unauthorized visit” in to this, but I see no reason to believe that the OP (and fellow readers) would know about and be dead set against the legal options.