The check is impossible. I don't know if you've used the software, but you can generate addresses offline. Even if this wasn't the case having more people making ever larger numbers of comparisons to protect against one person losing the coins in one address less than one time before the heat death of the universe is crazy.
What's to stop me from repurposing my miners to continuously generate new addresses? It doesn't seem like it would take long to generate a significant chunk of the key space.