It's not much of a problem if you're using Bitcoin correctly (ie, not reusing addresses).
That can't possibly be your proposed solution to this problem - "Just never use a bitcoin address more than once"?
While it makes sense for privacy reasons, it shouldn't need to be done just so you don't get your coins stolen.
If for example I give someone a bitcoin address so he can make recurring payments of some sort to me, I need to reuse that address. Everything else would just be a major pain in the ass.
You can get every transaction which has been sent by that address and ensure none of its spent outputs have the same signature in the script. But the main problem is random number generation.
Even if you want to make recurring payments, you should still generate an address each time. Otherwise you seriously risk linking your address to your identity. It isn't a pain in the ass, its the best practice for anonymity, regardless of this current bad signature issue.