In the example you give, with "her and I" this fits with a different trend : perceived agreement needs diminish with distance. So, the perceived agreement need from the "grandpa left this" is stronger with the first part of the composite d.o. "her" than with the second part "I".
So if the go-to form is really "She and I got this from grandpa" then we can explain why the choice is "I" and not "me" for the second part of the d.o. while "her" and not "she" for the first part of the d.o.

But really, if the message cannot be misunderstood in spite of the agreement failure, it's not really a problem in informal speech. People just need to realize that written language IS NOT spoken language, which is why use of voice recognition for typing GREATLY increases the need for word-processing grammar checking - or for third party post-editing: this is why secretaries go to special training for learning to take dictation: they need be ready to do simultaneous interpretation between two different languages (spoken and written), while typing it up. That's like combining the very specialized jobs of Conference Interpreter and Official Stenographer!!!
Replacing that training with software is no mean feat, as these activities are major strength areas of the human brain, in that we can learn them well if trained - just like we can learn to speak a language even if we only hear samples that are full of contradictions.