farmers don't really make any money from it, and there's little incentive to grow more. In America, higher tobacco prices = farmers grow more tobacco. Not in Cuba.
So demand for Cuban cigars outweighs supply, which creates an opportunity for counterfeiters to make fake Cuban cigars and sell them at premium prices. I doubt the counterfeiters even need to send the cigars to Cuba to get the stamp - but there's probably some official they have to pay off to look the other way. (The Cuban cigar-makers are all government-owned because private enterprise = no-no, so you'd expect them to go after counterfeiters). The counterfeits might be especially common in Latin America where people don't have as much money to spend on cigars - just like how fake iPhones and handbags are a lot more common in China than here
As for why Honduras doesn't develop its own premium cigars - that's hard to say for sure, but I expect there are a few factors. Everyone "knows" Cuban cigars are the best, in the same way everyone knows French wines are the best and Russian caviar is the best. Smoking them signals affluence and success in a way smoking other cigars doesn't. Then the embargo has helped build a mystique about Cuban cigars. It's hard to build up a new brand against all that.
But I think a bigger factor is that the people involved are basically running a criminal racket - they have a nice, comfortable operation where they grow tobacco and roll cigars with cheap labour, pay off the right people and sell at a high price. They probably think it's more profitable and less risky to keep doing what they are doing than try to convince Americans to smoke Honduran cigars, which would be a lot of hard work.