But not secure enough? Then just transfer you wealth from one to another address every few minutes.
Moving your wealth will not have an effect, in your example you are just as likely to transfer your money into an address controlled by someone else as someone else gaining control of your address.
The real solution to collisions (not that it is a real problem anyway) is to spread your wealth over as many Bitcoin addresses as possible. If it takes a trillion x trillion years to have a 50% chance of getting the correct key to an address with 50,000 Bitcoins in it, the attacker might not bother if the 50,000 Bitcoins were stored in 50,000 addresses of 1 Bitcoin denomination. This will mean the attacker will have to expend 50 x trillion x trillion years to get all those juicy Bitcoins.
- you want to find a private key to any address, not to one, to get a collusion
- checking balance cost you time,too
The checking of balances will cost time, and you might expend a trillion years to only find 0.004 Bitcoin. The best thing to do is choose a valuable target and focus every key attempt on that address.
If we now focus on the FBI address, the gain for all that hashing might be worth it (for an attacker capable of turning the entire energy of a star into pure computation.)
This way we do not have to check the balance every time and we can eek out more efficient computing.