but the odds that I and others even reached one with an already used balance proves that private key collision is a common occurrence even given the trillions to 1 odds.
There's only one way to prove a private key collision: show 2 different private keys that both produce the same address. Nobody has been able to do that yet.
You can't brute-forcing a random private key. The only way to find it, is if it's not really random (or if someone leaks it).