The whole point of the iframe is that it prevents the code from inside the iframe (ie the payment handling code that sends data to stripe) from having access to

The whole point of the iframe is that it prevents the code from inside the iframe (ie the payment handling code that sends data to stripe) from having access to the parent page's data. Sometimes the CC info isn't the most sensitive info a user has given that website (particularly for a service that manages your online backups).