CAPTCHA form not visible, after applying theme

I was facing the same issue before and in my case it was caused by my theme's customer_account_login.xml file.

For example, if your theme is extending Magento_Blank theme (which in most cases it probably is), then you don't need to copy the entire contents of the customer_account_login.xml file to your theme to make changes to it --> this will just "bug out" the CAPTCHA form.

The proper way to make changes is to use:

• <block and <container> elements to add new elements (blocks or containers)
• <referenceBlock>, <referenceContainer> to add new elements to existing ones, change their properties or just remove them
• <move> to move existing elements in the layout

You can read instructions here on how to do that: http://devdocs.magento.com/guides/v2.3/frontend-dev-guide/layouts/xml-instructions.html

If you are facing the same issue, you can quickly test it by renaming or removing your theme's customer_account_login.xml and clearing cache.

Then you can make the customizations the proper way based on the official documentation.