> How would the ability to type an arbitrary amount of numbers, or letters, in a credit card number field lead to higher conversion?
Sure - I'll bite. But I'm also going to point out that you're swinging to the other end of the extreme. Obviously no one in their right mind would just allow arbitrary input...
Clearly every CC number can be represented by numbers alone (by omitting the slashes). People are absolutely familiar with this and often will omit the dashes in their fields all together without any filtering of characters. Personally I key off of the "keydown" event on that field and e.preventDefault/return false on anything non-numeric. In the future, I hope the "inputmode" HTML attribute catches on with non-Chromium browsers - that would eliminate my need to do this.
After the number is entered, or (personal preference) before the form is posted, you do a simple Luhn check and show a dynamic error message RIGHT ABOVE the field saying "hey invalid CC num yo" - ideally you keep the "process" button and CC num field close to each other so this happens within the same document view without having to auto-scroll/anchor to the invalidated field.
Then, as always - ensure you have the capability to validate that data using the same rules on the back-end before it's allowed to be sent to your processor, or w/e.
There ya go - there's the "everyman's" approach to CC validation on the front-end.