In order to show that the current bitcoin key system is flawed, all that a person would need to do is show that there was a correlation between the relative position of a private key and the relative position of its corresponding public address.
Both the elliptic curve maths for going from private to public key, as well as the sha256+ripemd160 hashing to go from public key to address, are both deliberately designed to be
one way operations.
The only correlation is that they're deterministic (the same private key always results in the same address).
In other words, if you took the lowest possible private key, a 256 bit number starting with 00000... etc, and the highest possible private key, a 256 bit number starting with 11111... etc, and you were able to show that the two public addresses for those keys formed hard boundaries, i.e., that all bitcoin public addresses fell between those two numbers in some mathematical formula or progression, then you would be showing that an accessible formula existed to work backwords from the public adrress to the private key.
Not saying that it is theoretically impossible to come up with a feasible way of constructing a matching private key with
some given addresses (although extremely, astronomically unlikely). But in general, such a formula will not exist. For starters because it's
destructive: some information is lost in the process, and you can't magically restore information out of thin air.
You seem to think that for mathematical or logical reasons, there
must be some hidden correlation or formula that, once discovered, would allow you to efficiently reverse addresses back into private keys. This is not necessarily the case.
For example, suppose that the function that converts from private keys to addresses is a pseudorandom mapping: it's deterministic, but there's no specific order or correlation whatsoever. Or for argument's sake, let's say the mapping is
really random, constructed by sequentially throwing a dice a centillion times. Then this boils down to a huge (but ordered) list of private keys and their corresponding addreses. Well, guess what, we have such a mapping right here:
http://directory.io/Note that this is actually real: ALL private Bitcoin keys are in there, both used and new, current and future ones, along with their matching addresses.
So there's the function right there. It allows for very efficiently calculating the address for any private key, based on a simple (but huge) one-to-one mapping. Now, given this function, how does your argument apply that this 'must' be feasibly reversible in some way?