There is no actual way of "destroying coins". Even sending to an address with a private key that isn't known, a person can also get a lot (and i mean a real lot) amount of hashpower to bruteforce the key. Although it would be difficult, the coins are still recoverable.
Coins can be mined out of existence (miner selects a reward less than the max allowed).
Still coins sent to addresses with no known private key are effectively lost. No you can't brute force it with a lot of hashing power (not even all the computing power on the planet). If you could then Bitcoin would be worthless.
As far as I know, you can perfectly try and bruteforce a bitcoin address. By simply using VanityGen. Your odds will be next to zero, but that DOES NOT mean it is impossible. Also, how do you know that in the near future there won't be asics capable of doing so?