For me, my issue with Tina is simply, how would she survive during arcs like that? I could understand her joining in for those arcs outside of the main areas, and in a way, I could understand bringing her in for the Melk Arc and the Gourmet Temple, those are more relaxed areas, where she'd be more than welcome.
As for her in this arc, I'll admit she's growing on me. She's proving useful, and that's what's winning me over as far as she's concerned. Who knows, she may appear when we meet Zebra, or during the Century Soup tasting sessions, but it's a matter of knowing where to insert her.