Since iOS just added the ability to put any arbitrary app behind FaceID, you can be sure that Android won’t be far behind. They always copy each other.
And you can be damn sure that Obsidian developers won’t even consider working on it for Android now, as it would be wasted effort.
Honest question: Do you not understand that your notes can still be accessed from any other text editor app or the file explorer on your phone? Without the paid sync services, nothing ever leaves your device. There is no encryption. It’s your choice as a user which security measures you want to enforce on your phone.
IMO, locking the app with a password screen or biometrics, while adding some friction, would be quite pointless without full encryption. And depending on what an official encryption service would look like and how your keys would be stored, this feature could mean that you would be dependent on Obsidian to decrypt your notes which would lead to lock-in. (Similar to what one user said above about forgetting their password and potentially losing access to the data stored on the sync servers.)
Obsidian doesn’t necessarily stand for security. It stands for giving users agency and control. And I can understand why it would take them a long time to think about whether this is something they would consider doing and how they could implement it without sacrificing their main intent.
I mostly agree, but some people more or less regularly hand their phones or tablets to other people (their kids, for example) who aren’t savvy and/or motivated enough to go poking around in the file manager or navigating to a vault in another text editor. It’s mostly to keep them from tapping the icon and opening the app accidentally or out of curiosity and messing something up or seeing something they shouldn’t.
But I don’t think it’s necessary for Obsidian to implement it now that it’s possible to do it at the OS level on iPhones and iPads, and as @obsequious pointed out, likely to become an option in Android, too. And in any desktop OS, a guest account is a better and more secure solution.