Cash App won't let you add cash from your bank because they don’t have a way to verify your identity without a photo ID. This is important because Cash App is designed to be used in the same way that you would use cash in person—you load money onto the app, then use it when you need it. If you don't have a photo ID, there's no way for Cash App or any other financial institution to verify who you are and whether or not you're allowed to make a deposit into your account.
The easiest way around this is to get yourself a photo ID (like a driver's license) and attach it to your profile on Cash App. You can do this by going into the app settings menu and tapping "add ID" under the "security" section.