It is already possible to send bitcoins peer-to-peer. You can send money to friends and relatives in the form of bitcoins but an exchange will always be needed to buy and sell bitcoins because it ensures trust between two parties.
People use exchanges because they need to sell their earned Bitcoins to get fiat for spending or to buy Bitcoins with fiat that they earn. So, a more correct question would be "when will we be able to go 100% Bitcoin"? Right now it's not realistic to live on Bitcoin only, you'd have to take long trips to even buy all the needed groceries, and sometimes it would be just impossible to buy something with BTC.
In the future Bitcoin adoption should be higher, so in some parts of the world people will have a chance to use only it, but I personally don't think that it will be like that globally, especially if some countries will keep restricting its use.