But military service exemptions are largely about providing simple entertainment, even if it's not about enhancing national prestige...

Lee Chang-ho is the most immediate example.
There are many Go enthusiasts among politicians... Won Yoo-chul suddenly comes to mind, haha.
Regardless of whether they enhanced national prestige through the "Shanghai Battle" or not,
it's more that politicians, wanting to enjoy the pleasure provided by Lee Chang-ho during his prime in the sport of Go, were so excited that they granted benefits.
Before national prestige, shifting public opinion, shaping public opinion, and legislation—all of this depends on the politicians, seriously.
BTS is the core counter-argument for those calling for the abolition of military service exemptions... I also believe BTS has greater national interest value than those soccer or baseball nobodies, haha.
To put it bluntly, I think a big reason is that legislators have very little interest in "idol nobodies" themselves,
so it hasn't progressed to the stage of reviewing this more seriously from a national interest or grand strategic perspective, seriously.
Even for me, if I were a legislator,
I'd want to see Kim Do-young performing in the Majors so badly that if I had the authority, I'd just grant him an exemption, haha.