Once people understand what it takes to reduce a number with 156 zeros down to a manageable size, they usually begin to comprehend why "I'm thinking of a random number" is actually a very safe way to store your Bitcoins.
This is actually the point of this whole thread!
But:
1) the real measure of how random is an address is 2^160, not 2^256, because there are 2^96 different private keys for the same address
2) if you reveal your public key, it takes only about 2^128 guesses (just to simplify) to steal your bitcoins
At this moment the hash rate of bitcoin network is about 2^67 hashes/s, i.e. about 2^92 hashes/year.
Generating a hash is faster (so far) than generate an address from a private key, it's just to have an idea of what size of numbers we're talking about.
We would need a computation power 2^36 bigger than the current entire network to crack an address in 1 year. It would take 36 consecutive doublings to get that power.