Tab key is commonly used to quickly get to the most used text inputs (such as searchfield, or textfield). But XenForo doesn't have them. I think search bar and message text field should have tabindexes, that way we won't have to scroll down to start typing a message.
Tab indexes have uses in some scenarios (and we do use them there), but adding them on every input would be pointless and very hard to maintain. Additionally, tabindex is actually for all elements and affects keyboard navigation, so I believe this would have a negative effect on accessibility.