Your solution might be a trick.
But what worry me the most is that blockchain.info doesn't provide a solution to this problem like in their old wallet.
There is no guideline on how to recover your fund in case the site go down or disappear.
When you search for backup into the FAQ and blog section, it only give as results the 12 words recovery process in case you loose your password and also they say that it can be use in case blockchain.info disappear but no explanation how to use those twelve words recovery phrase in order to get back your BTC if Blockchain.info go down for ever or a long time.
Old version was providing a way to download the private key (encrypted with your password) along with an explanation how to recover your funds in case blockchain.info go down.
I agree ,they didn't give a decent amount of information for users for what comes to this new wallet. It's probably best to contact them and ask them about this.
I just searched btw , It seems like they are going to implement the signing messages soon : https://support.blockchain.com/hc/en-us/articles/210353833-What-is-message-signing-and-how-can-I-do-that- which means that users will have control over their private keys so I assume exporting private keys will come with it in the future. Good luck !