It is not recommended to use closed source wallets because you cannot review the code, and not because all closed source wallets are unsafe, but we can agree that it is much better to use a well reviewed open source wallet, than a closed source wallet that the code cannot be reviewed. Too many people wrongly think that open source automatically means safety, it doesn't.

Ledger, just like Trezor is a hardware wallet that has been 'around' for a long time, and even though they were closed source, their devices were still recommended until they launched the ledger recover service, as a company that should help you store your keys offline, they ought to know that it is unsafe sending it to third parties, when they initially said it couldn't leave the secure element chip. This is the main reason why Ledger shouldn't be recommended.