Let's take a quick look at what they might do with your KYC documents.
People they will share your data with:
Companies within the Blockchain corporate family located in the United States and the United Kingdom, in order to provide the Services to you.
Cloud service providers to store certain personal data and for disaster recovery services, as well as, for the performance of any contract we enter into with you.
...
We may transfer your Personal Data outside the EEA and the UK to other company subsidiaries, service providers and business partners (i.e., Data Processors) who are engaged on our behalf.
So any of their subsidiaries, and any third party companies they hire to provide a service to them or store and process your data on their behalf. So pretty much anyone they like.
We will make reasonable commercial efforts to ensure that they comply with such policy or requirements, however, where not expressly prohibited by law, we will have no liability to you, if any person fails to do so.
If one of these third parties decide to sell your data (as was the case with Coinbase) or are hacked for your data (as was the case with Binance), Blockchain.com will take no responsibility.
Even if you think every member of staff at Blockchain.com can be completely trusted, what about all the staff at every unknown third party they currently use or will use in the future? Do you really want your KYC documents stored on the cloud by an unnamed and unaudited "cloud service provider"? It's impossible to count the number of times that cloud servers have been hacked or compromised.