"Not your Keys, Not your Coins" it applies to famous web-wallets such as Blockchain.info wallet, where any mistake/bug (whether by you or through them) can lead you losing your money without compensation, and how will it be with a wallet that controls your money, it is like trusting an unknown bank without proof of ownership.
If you do not think this is so bad, read the following:

 - cryptonator.com is a big scam ! i lose near $ 2000 ! extreme alarm
 - Cryptonator is a SCAM!! BEWARE!
 - Cryptonator - Reviews

try Mycrypto wallet.

It's like bank transfers. You are enduring for the highest fees and you can not choose.