Yep, that is certainly the case now. My formative sports years were 2001-2006, however, and I actually do remember feeling like this was a pretty hyped game on the national stage. From 2000-01 to 2015-16, it was on one of the main two ESPN channels. Since then, it has only appeared on ESPN2 in 2017-18, and it has been on BTN or SECN three times.
A lot of this comes with the competitiveness of the teams, as
just as we started to make a turnaround, Mizzou really went downhill. From 1998-99 to 2005-06, at least one team was ranked in every single game, with BOTH teams being ranked in half of those years.
Really, are there any other current non-conference "rivalry events" that would even come close if both teams were consistently good? Braggin' Rights is very much in the mold of several traditional football rivalry games at neutral sites, such as Georgia/Florida (Jacksonville, FL) and Texas/Oklahoma (Dallas, TX), where fans are split at midfield.
If there is another basketball equivalent, I am honestly unaware of it. Braggin' Rights is special in that aspect, and when you add on the years of tradition, the unique "Christmas feel" and the bad blood between the fan bases, it really is a special event.