I've never felt comfortable with those paper tags which you have to fill in an address and contact info in order to be useful. In this day and age, do you really want to hang that kind of data out there?

The AA tags are minimal - only the name. AA is the only one who can extract the more detailed data, and the plastic ties are stronger than the string of paper tags.

They also last longer, so I don't have to replace them regularly.

So I really think it's an useful benefit to have elite luggage tags, beyond the show-off factor. If you dropped to PLT but didn't get PLT tags, by all means keep the old tags on. It'll still server one purpose.