I eventually did what you suggested. The issue I found with this is that usually across from the copyright is our attribution link, and we'd often have clients

I eventually did what you suggested. The issue I found with this is that usually across from the copyright is our attribution link, and we'd often have clients that didn't update their website's "look and feel" for many years. The year would be current, and it could make it appear as if an old design was "current".