Some exhanges handle a 0.001btc fee which is pretty high!
It's not high at all. It's a common withdrawal/external transaction fee. The network fee is hovering between 0.0008-0.001 BTC for quite a while now, so from there it only makes sense that services charge these fees. If you seriously believe that services will grant you cheap external transactions, you're very wrong on that. It would allow people to abuse their platform just for the purpose of sending cheap transactions, and thus save a couple of bucks per transaction. It's a business after all, and a business is in the game to make profit, and not to function as some sort of a charitable organization just because people don't want to pay appropriate network fees.