There is something to consider. It is korea. Reputation and appearances matter a lot (actually all around the world it does). He is a lawyer, has money, probably graduated from a good uni. You would be surprised to know how many cases are delayed to be resolved cause cops would rather not "bother that respectable citizen with nonsense". The same way poor folks are arrested no questions asked, rich folks receive the opposite treatment.
Also in investigations you need to bring a "motivation" to why the murderer did that. In the case of mentally ill people like inseop it is difficult cause how you gonna say a rich lawyer killed his sister for a pen? His motives are too weird cause his brain is not normal, but at the same time no one knows he is mentally ill and he looks just like a sane respectable person.

Once again it seems quite literally the only reason Inseop got away with this for so long is because no one thought to inspect him. He is sloppy as fuck really it’s insane. All his life he probably was told he was sooo smart and never being caught for killing his sister probably went to his head big time.