The damage was about $4000. The court gave him suspended sentence, considering his old age and the fact that he had no prior record. However, the compensation/fine of $13,000 he was forced to pay drove him destitute. So he got angry again and went back to his protest by torching a landmark.
Obviously he was seriously misguided and angry man. The reason he got caught so fast is that police started to check those who had prior record on damaging historical landmark. He is not a beggar or homeless roaming around the place, as it turned out.
As you said, they do not have to go far from Namdaemun to find beggars or homeless. These days, Seoul Train Station works as a night shelter for homeless. If you go there early morning or late night, you may see hundreds of them dozing at the chairs of the main lobby.
I came across one of them right after 4am when I got off a train. There were a few really disturbed people, who went around yelling non-stop. One of them came to me and taunt for a few minutes for no reason.
If police behaved as you said, that would be the first place to go. There would be more than one real nutcase, and frame him as the culprit.
However, would it have worked? I don't think so. Based on the evidence on the scene, it was a premeditated act after some planning.
There are some high-profile unsolved cases in S. Korea. Multiple murders of women over several years. And double murder of kids more than 10 years ago. I wonder why police was unable to find a convenient scapegoat in those cases.
There is some work to be done about comparing possible finger prints on the lighters found at the scene with the suspect's fingerprints.
Apparently, the suspect did not bother to cover his tracks carefully. He casually walked out of the scene and took a cab and went to the place of his son, and stayed there overnight, and went home the next day. He now lives in Kanghwa.
So your charge of rounding up vagrants and beating the crap out of them until one of them confess is not true.
Reportedly he case the place in last July and December, so that he can presumably figure out how to go in and out of the place, undetected. The place has security cameras, and daytime security personnel. He was able to elude all of them, by picking the right time and the route of entry.
I think you jumped the gun on this case.