No 100% sure I agree with you, although I'm interested in learning. There is a very common misuse of I instead of Me in a lot of English speakers. The easy way to figure it out is if you put the two together, would you replace them with WE, or US. I should be used where WE would be, and ME should be used where US would be. So for 'you and I' for example. You and I are going to the shop, is right because it would be WE are going to the shop. Thank you for meeting with John and I, would be wrong as it would be replaced with US, so should be 'thank you for meeting with John and Me. I feel You are better than Me, is right. But only 97% sure :)
The "rule" you are talking about is not really what we should go by here for 2 reasons.
The overuse of "I" addressed by your rule is in the phrase "you and I," which is why you're supposed to try replacing it with "we." But that is not what we have here.
That "rule" is actually a shortcut to the real rule: you use "I" or "we" for the subject and "me" or "us" for an object. So, it should be easy to figure out which to use if we can figure out if "me" is serving as a subject or object in this construction.
That is the challenge, though. Technically, this sentence is a shortening of "you are better than I am." The "than" is a conjunction connecting clauses, which have at least a subject and a verb. Since it's been shortened to "you are better than," though, it sounds funny because there's no verb in that clause. That applies with both we/us and I/me, which is why it sounds right to you to say both "you are better than me" and "you are better than us." One cannot be used to prove the other.
So, in the end- "you are better than I" is "more" formally correct, but it doesn't really matter because the formal sentence is "you are better than I am" anyway. "You are better than me" sounds better (to many, though not all) because it doesn't have a subject dangling with no verb.
It is a question of prescriptive vs. descriptive grammar. Most textbooks still insist that "I" is correct in this construction -- "better than I (am)" -- because the verb following the subject "I" is understood, but this rule is generally not observed in spoken American English. Merriam-Webster tries to stay on top of the changes in usage, but a lot of English tests are still very prescriptive. It's good to know that both "than I" and "than me" are used.
Those would be the correct forms according to conversative English grammar.
I'm fairly sure my father would say those.
They're not natural forms for many English speakers nowadays but I'm sure there are some who use them naturally and others who have been taught to use them and now use them because they (think they) are supposed to.
I never gave much thought about this until now, most probably because English is my third language. You are right that ''better than she'' and "better than we" are not used very much but I'm pretty sure they are grammatically the correct forms. We here in India, are taught Queen's English that's why I guess we use "better than I" instead of "better than me". But we mostly use "better than I/she/we am/is/are". I think that it is American or more precisely Hollywood's influence that we are not speaking proper English and grammatically correct English sounds incorrect to our ears. For example many people use double negatives in their sentences like its grammatically correct 'I ain't doing nothing' 'I ain't going nowhere'. Moreover I never quite knew what is this "ain't " (and many other things) until I started to watch English movies etc. And I still don't know if this is proper English. Anyways. Peace.