As you mentioned 'Exchanger' in your sentence, I will start with that. So you really believe what exchanges show as fees is actually the fees? No, it's not! What exchanges actually do is that they send Batch payments and earn huge on from users on the name of Fees.
Ok, now coming to possibility to reduce fees. The amount of fees is not fixed by miners, nor does it pop-up randomly from somewhere. Actually it depends upon Demand/Supply rule. Now suppose there is single seller with Apple and 5 people wanna buy that Apple, every buyer will try to supersede other's bid to own Apple and as a result price of Apple will go many times more than initial price. Same is happening to Bitcoin fees. In order to get transaction confirmed before others, people are giving out more and more fees and as a result we reached a state of congestion and Very High Fees.
The way out from here is possible if people start using the concept of Standard fees than Competitive fees. All wallets should start using a fixed fees concept so that all transactions broadcasted have equal preference and concept of adding transaction to next pool become 'Matter of Chance' rather than 'Matter of Choice'.
Actually, bitcoin transaction fees can still be reduce and there are some ways to reduce bitcoin transaction fees to get payment to reach to the recipients or should be registered on the bitcoin ledger by reducing the transaction size. The allowed amount of bitcoin transaction fees is proportional with transaction size which has nothing to do with the sending amount. In order to reduce payment fees, you must have to reduce the size of transaction.