I think the cause of the delay is both the family illness AND the routing issues, but I believe these routing issues are a direct result of the illness in Edge's family. There's every indication that the tour is now going to start in the Southwest, meaning that the tour has been re-routed to go from west to east, instead of the reverse.
It's a fact that Edge has a home in Malibu. I believe the re-routing is based entirely on allowing Edge to stay with his family at his US home in Malibu, while rehearsing the tour as well as playing shows in the Western US. On past tours, U2 has already used LA as a hub city that they fly out from on the afternoon for shows in San Diego, Phoenix, Las Vegas and the Bay Area, while flying back to LA right after the show ends.
By allowing Edge this ability to stay at home and only fly to concerts, it allows the tour to continue, while Edge is able to spend the majority of his time with his family. My guess is that Edge feels that whatever this illness is, that it is treatable and not enough of a reason to cancel a tour.
While Edge and the members of U2 do not need to earn all this extra money from doing a tour, I'm sure they feel some type of commitment to the crew members that they have retained for the next year and to Universal, as well as the fans,to follow through with the tour.
I won't be at all surprised if when the dates are announced soon, that the majority, if not all of the first leg, is based in the western half of the US to accomodate Edge being able to stay at home on almost every night.