I think they do a great job in the series showing that Jiwon's hesitancy to go public is more about trying to protect Jeongyu. The webtoon goes into more of what he's had to deal with in the public eyes as the "Nation's Grandson", going back to his early days as a kid.
Jeongyu has had local success and is just starting to get national attention at the college level ... plus he has the kind of confident personality that allows him to brush off what others may think. But he doesn't know what he doesn't know or how bad things really were for Jiwon. Or how terrified Jiwon is about bringing that same kind of nightmare to Jeongyu.