Bitcoin security, what is wrong with my thinking? Lets assume I keep generating random public keys with their matching private keys and never use them.
Severals years later I am checking for positive match against the blockchain for all my generated public keys.
If a match is found that means someone is actually using a public key I generated in the past and for which I know the private key.
I should then be able to gain control over someone else wallet even in the case of a paper or brain wallet.
Best regards,
Thats right, if you got the private key you got access to the bitcoins on it. You dont even need to wait until someone starts using this key, you could also randomly find a key which is already in use by someone.

BUT:
Bitcoin addresses are 160 bit hashes of the 256 bit private keys, so there are 2^160 or about 1.460.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000 possible addresses. You will notice thats the possibility is pretty much nil.

For more information you can read this article: http://www.miguelmoreno.net/bitcoin-address-collision/