I think it just keeps it much more simpler to go with Capitol, because they're going to be doing so much with all the classic songs. They've probably got several archival things going on in the next year, and it just puts a big red bow on the top that they're using the same record company.... they can just go full blown and endorse everything, all the time, by the same people involved, etc. So every press release can mention the tour, and the old songs, and the new songs, etc. and every poster can be similar, etc.
True, it is very consistent for them to stick with Capitol, and as with That Lucky Old Sun, Capitol is part of the overall branding. Still, I wonder if they just went with Capitol by default, or perhaps if they considered going it alone or going with Warners, etc...