(If you meant that first part in jest, please ignore this)
No, being a Texan in no way insures you an interview spot to Texas schools. I was interviewed/accepted to 3 Texas schools out of 8, so I got no love from 5 schools. Granted there are others with a much higher GPA than I, but same thing, you're definitely not guaranteed an interview to the Texas schools.
Anyway, about the essays, they are completely optional, and if you felt like you had nothing meaningful and worth the time to write, then you made the right choice in not writing anything. These admins read more essays than I ever hope to see, so I think they're probably somewhat greatful that you didn't bs a couple of essays just for the sake of filling up space. Bottom line, don't worry about it.