Is this a common situation nowadays?
No.
As Herektik said, this only applies if you have a lot of small inputs, which do increase the size of your transaction.
The transaction fee is based on the size of your transaction. Bigger size -> higher transaction fee.
What is the workaround?
The easiest would bet to export your seed and import it into any other wallet (e.g.
electrum) which lets you set the fee on your own.
If my money is in the blockchain, how can blockchain.info control it?
Your BTC's are recorded on the blockchain.
But the private keys to access these BTC's are stored on blockchain.info's server.
They claim that the private keys are only stored encrypted on their server, but to be sure you'd better use some non-online wallet (e.g. desktop- / mobile- / hardware wallet).