Error 'Insufficient Privileges' when creating a reCAPTCHA API Key Pair in Web-to-Lead/Web-to-Case

When using reCAPTCHA to prevent spam Leads, you should enable Quick Create to prevent 'Insufficient Privileges' errors when creating a new API Key Pair.

Steps to reproduce:

In Classic:
1. Click Setup | Customize | Leads | Web-to-Lead | Create Web-to-Lead form
2. Click 'Include reCAPTCHA in HTML'
3. Click the reCAPTCHA API Key Pair lookup button.
4. Click New and then fill out the required fields.
5. Click Save.

In Lightning:
1. Click the Gear icon then Setup | Feature Settings | Marketing | Web to Lead | Create Web-to-Lead form
2. Click 'Include reCAPTCHA in HTML'
3. Click the reCAPTCHA API Key Pair lookup button.
4. Click New and then fill out the required fields.
5. Click Save.

You should then receive the 'Insufficient Privileges' error.

Note: This is working as designed