It depends on your knowledge and regional location. There are commercial carpenters, teacher of carpentry and carpenter helpers just to name a few. Benjamin you have the mind to create your own business and pitch your skills to the right buyers. You don't need an organization to show the world that you know how to work with your hands in a dexterous manner. At the same time if that is your choice, the platform is beneficial to both parties. America changes every 4-5 years in fashion, style and technology so you will always be an asset as a carpenter. Of course there will be an abundance of jobs. They just dont advertise it as much because they want people already trained ready to work with no real supervision. I wish you the best on your journey.
A carpentry position is a very good profession. Possible you could enhance your skills by taking classes with local union halls until carpenter jobs become more in demand. Agree with the one person who wrote that carpenter jobs really depend on the city and area where you live. There are carpenter jobs out there, but you really need to network. It also depends if you are interested in a big general contracting company or small maintenance companies.
Best in your search.