In Canada, the SAR teams are all volunteer, they get little or no government support. If you're lost in the wilderness, police may bring a sniffer dog to your last location, but they won't go looking behind bushes for anyone except a small child. SAR's have formed for that reason.How realistic is the expectation that the US should send an official search team to locate its citizen that goes missing abroad? Has that happened in other cases?
I've noticed in California, some SAR seem to be paid employees, but IMO that's very unusual.
Since Greeks aren't into hiking, etc, there seems to be no SAR groups.
As far as Consulates, IMO they stay far away from offering support to individual tourists for anything except passport/visa issues, and providing names of lawyers. They absolutely can't help everyone, and they won't play favorites and help some but not others.
JMO