I have a United 1K card. I hardly ever show it: the folks at the 1K centers I frequent recognize me, the FF number is with my travel agent and stored in the United connection software, and the boarding passes display the status so I just show my boarding pass for early boarding. While non elite members may switch between United and delta (which they could for most routes do anyway before the alliance), elite members still have strong incentives for choosing their respective carriers. I also read in the Wall St Journal that codesharing between United and Delta has been scrapped or delayed. I would think that brand loyalty is still alive.