I'll have a crack.
What a lot of the most popular leagues and teams globally seem to do well is create an attachment to individuals, not just the team/competition. Maybe it's a chicken or egg thing - having top level 'superstars' certainly helps with fan connection - but I don't think it's wild to suggest that more could be done to help foster this.
I was having this discussion with a mate the other day - you can buy an individuals's jersey (with name and number) for just about every other major sporting team or code, but not rugby (union or league for that matter). Looking at NBA as an example again, some combinations of name, number, and team have their own lore that also gives insight into the person wearing it. Rugby is obviously more limited due to the numbering being position-based, but I don't think the point is entirely moot.
Some of the Wallabies' WC social content has been pretty good and starting to show the players' personalities, but there's definitely more ways to go. Formula 1 (both the organisation and the teams themselves) do it very well imo - the vast majority of the content is about the drivers and their personalities. Granted, this is much easier when you've only got two people to promote (excluding other staff who have their own followings, e.g. Toto Wolff).
Funnily enough, reflecting on it now, I think this is something the Reds' did very well in the ~2011 era - they hitched their wagon to a core group of marketable and already popular players, and went all in for as long as they could with branding, advertising, and merch. Guys like QC (Quade Cooper), Digby Ioane, Genia, Higgers, Radike, and the Fainga'a twins all did heaps of marketing, featured on the 'My Reds Family' bumper stickers, and had their own merch lines; QC (Quade Cooper) had a shirt in the members packs, Radike had afros handed out to members of the crowd, I'm pretty sure the twins did something twin-related, Digby had the breakdancing turtle thing, etc.
I couldn't say what the best methods to build these individual attachments are, but I think it's definitely something to start thinking about.