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.
Lets say you generate 16 billion addresses per second.
Lets say you do this for 400 years.
You now control 1.38196 × 10^-28 ratio of the addresses.
That's 0.0000000000000000000000000138196% of the key space
Calculation.
That's not really a significant chunk. I think there is more of a chance of a gene mutation that would allow a baby to be born as an adult with superpowers, then he or she could just rob banks.
Basically pretty much EVERY bad thing you can have happen to you has a larger chance of happening than an address collision.
EDIT: I must add that generating 16 billion addresses per second is beyond what a standard person can do. 16 billion addresses is 16000000000*160 bits or 298 GB minimum for just the public key portion in your wallet for
just one second of those theoretical 400 years. I think most people would run out of resources fairly quick.