The questions you ask are important ones. The Polyglot community has given you some reasons for learning languages no longer actively spoken. I would offer a few reasons for learning languages spoken by smaller living linguistic communities (you mention Cherokee).
(1) It is fun! Typically, these languages will be well outside the usual constructs of the European languages, and will stretch you brain in ways you didn’t even know were possible. If you do it right and stick with it, you will learn to see and process the world in new ways.
(2) Your energy and passion are greatly needed! In North America, there is a powerful language revitalization program currently underway with a number of Native American languages. A few examples are Lakota (Teton Sioux), Cherokee, and Navajo. Again, you may find these challenging if you have only played with European and Asian languages, but they are also incredibly rewarding if you stick with them.
(3) There are now plenty of materials out there. There are Cherokee communities in North Carolina and Oklahoma, at least one online radio show in the language, and numerous books available. The Lakota have a great online dictionary and a super cool series of Berenstain Bear videos available on YouTube for free. The Navajo have at least two online radio stations (KGAK, which is my favorite, and KNDN). There are also some really cool verb conjugation books available on Amazon in the form of the “Fun With Navajo Verbs” series, and free software games on the www.accessnavajo.com website for download (you need to install a Java Runtime Environment (JRE), which is quite easy to do.). And these are just the tip of the iceberg! I suggest you take a look at some of the free materials that are available and see what resonates.
(4) Getting involved with people from these groups can be quite rewarding. My ancestors came to North America from Europe back in the 1600s and 1700s. I spent a few years in High School in France, and then traveled to the Middle and Far East as a young man. I ended up living the better part of a decade in Taiwan, Jordan, and Japan, learning the local languages as I went. I did not really “discover” the above three languages until my middle years, but boy what a discovery. I have been working with a Navajo scholar to develop some sorely needed verb conjugation books (the “Fun With Navajo Verbs” series mentioned above), which had been giving me a reason to travel out to Arizona and New Mexico once a year or so for the past few years (a plan that is currently on hold for obvious reasons). The point here is that there is actually somewhere to go with these languages once you learn them, a ton of fun to be had, and some real good to be done if you are motivated. I can tell you from personal experience that helping to (re)build linguistic communities is a blast!