I understand it to be as follows:
To play in the Classic Cup, a team must play in a SCYSA sanctioned league. The league must be comprised of at least 4 teams, and play each opponent once. This is where the 3 games comes into play.
Further the team must be comprised of properly rostered classic players. A recreation team can play in a SCYSA sanctioned recreation league, then roster the team as a classic team prior to the appropriate deadline, and be able to compete in the Classic Cup.
So, the Classic Cup is open to any team not participating in the SCSCL, or RIII Premier, that has competed in a SCYSA sanctioned league.
Coach P, in your scenario of a rostered Classic team choosing to only play in tournaments, if your team is rostered as a Classic team, the only SCYSA sanctioned leagues available to them are the PMSL, SCSCL, or RIII, and depending on age, Palmetto Classic.
Back to the original intent of this of location. Location is an easy part of the equation. The harder parts are getting the volunteer support to host it. It is very natural for everyone to advocate convenience from their personal perspective. Often times the very ones that strongly advocate convenience allow others to step in and work to provide for their convenience.