Among the primary missions of the ANA is education, and its annual Summer Seminar is held on the campus of Colorado College each June. While the college has been making things a little more difficult for the ANA in recent years, it's still a viable setting for this popular event. I've been going since the early 1980s and instructing there since 1995, and I can attest to its popularity and usefulness.
As for the ANA's numismatic holdings, many of its coins and notes are teaching tools in the various classes. The grading and counterfeit detection classes in particular sell out way in advance, and the coins utilized are almost entirely those in the ANA's possession. It would be challenging to conduct these classes without them. Many of the instructors are coin dealers, rather than collectors, and they can't afford to retain hundreds of coins simply for their annual classes. Even if they did have these coins in stock at the right time, it would be burdensome to travel with them and might discourage further participation. Having a standing array of teaching tools is essential to the ANA's educational mission.