The Copa usually has 12 teams. They expanded it to 16 for the Centennial. But since CONMEBOL has only 10 teams they always invite 2 extras so we could go on occasion. The USA -- at least according to Wikipedia, is often invited and usually declines because of conflicts with MLS. "The United States was invited to every tournament between 1997 and 2007 but frequently turned down the invitation due to scheduling conflicts with Major League Soccer. However, on 30 October 2006, the US Soccer Federation accepted the invitation to participate in the 2007 tournament, ending a 12-year absence."
https://en.wikipedia.org/wiki/Copa_América
Maybe if we had accepted during that period we would not have been invited the subsequent tournaments. Can't say. This was our first appearance since 2007 and I don't know if we were invited in between and the wiki doesn't say.
Wiki lacks a broader insite into managing a national team. The Copa and gold cup usually run one after another in the calendar. If we were to send our best team to the Copa, we couldn't ask them to also compete the Gold Cup, which we do need our best team to qualify for Confedirations Cup. True, over the last decade only one GC determined the CC participant, but I'm sure USSF saw a long run (and possible win) in the GC leading in the the World Cup as a better opportunity for the team to gel and gain confidence.
Sorry if this is getting tangential.