I meant, one can generate such private keys "hoping" it will match an existing one then he/she can sweep it into a new wallet, eg. like an attacker would do.
You can always start with a good randomly generated private key then do some random changes using that initial key as seed. Is there any protection for such attempts?
Still I don't understand why uniqueness is not ensured by design, one centralized mirrored server could track all transactions queue.
People are winning lottery from time to time...from those cases when people are complaining about stolen funds, are they really sure it was their fault of just the current design?

It is impossible to have a security system which is impossible to hack, and as far as security systems go, bitcoin's is pretty darn good.

Given that most 2FA codes are 6 digits long, there is a 1 in 10⁶ chance of someone guessing your 2FA code.
Assuming an average house lock as 8 tumblers, and each tumbler can adopt one of 10 positions, then there is a 1 in 10⁸ chance that someone will be able to guess your exact house key shape and unlock your door.
Given a standard credit card has a 15 or 16 digit number on it, there is at most a 1 in 10¹⁶ chance that someone will be able to guess your credit card number.
If you use a password manager to generate a long and totally random 16 character password, drawing from the full ASCII 95 character set of upper and lowercase letters, numbers, and symbols, (e.g. CY\u4"=t{rV%;N9S), there is a 1 in 4.4*10³¹ chance of someone guessing it.
The chance of someone guessing your private key is 1 in 1.158*10⁷⁷.

The chance of someone correctly guessing your password, your 2FA code, your credit card number, and the key to your house simultaneously is 4.4*10⁶¹, which is still around 2 thousand trillion times more likely than them guessing your private key.