To me the only reason to achieve elite status is to actually use the benefits. Otherwise it's just a waste. It would make no sense to get to diamond (or any other status) to then switch to some other program and start all over again at the bottom.

However, there are many people who do go for multiple status. If I was doing it and my choices after reaching diamond were staying at an Embassy or a Hampton where there is little in the way of benefits or getting status at another chain then I would go for the second status. If however my choices included properties known for upgrades, etc, I would enjoy the benefits.