Argh! This should have been canon. They had a bunch of interesting connections, including Tatsuki being able to sense Orihime across worlds, despite not being particularly sensitive otherwise and Tatsuki herself being an interesting character that seemed to be slowly dragging herself up the power ladder via skill and determination, rather than luck and genetics. She could have been a great counterpoint to Ichigo! Instead, she's all but disappeared and Orihime is just another one of Ichigos potential interests.