If such a purse existed, then there would be a high risk of losing all the money!
And why is it necessary?
The exchange has wallets, just for trading)
it is not at all a complicated thing to create! I have never checked out either one of Exodus, Jaxx or Coinomi to say anything about them, but the process is pretty simple using either one of these APIs like the shapeshift or simply creating a decentralized exchange among the users of that wallet.
for example when you run the wallet you become a peer on the decentralized network of exchange. then you can see all the others and their bids and asks and either tell them your bids and asks or just accept one of their offers and fill it.
this way you own your private keys and nobody can rob you. but when you use exchanges (the centralized ones) and their wallets you don't have the private keys and they easily rob you as Cryptsy, Mt Gox, Bittrex,... have already done.