Also how computational expensive is it to create a new address each time?
Your average modern processor should be able to generate just shy of 1 million private/public keypair combinations per second.
Collisions are also practically nonexistent, taking 28.23 trillion trillion trillion centuries to brute-force if you singled in on a single address (and that's assuming one hundred trillion guesses per second, around
). This time goes down as the array of pubkeys you're trying to crack grows, but the processing slows down as you have to check every generated privkey against that array. I don't know where the trade-off is.
Still, that's.. uh.. 2823000000000000000000000000000000000000 years. Earth has existed for 4540000000.