Did the economic benefits for the American frontiersman, cowboy, miner, farmer, and fur trader make the exploitation worthwhile?

Yes, the economic benefits for all these professions made exploitation worthwhile. Without some of these people, such as a miner or a farmer, America's expansion and economy wouldn't have been as successful. With the miners' gold, and the farmers' food and goods productions, the 1800's just wouldn't have been as important.