I guess a lot of time when someone is gone for 12 hours or so, they often are just out somewhere and there's a misunderstanding. They usually show up the next day or something.
Starting a search costs a lot of money so they hold off to make sure there really is an issue.
Personally, I think it should be done on a case by case basis. If something really unusual is happening then the search should start right away. For example, in the US they do a Amber Alert (radio/tv msg) almost immediately if a child goes missing. It's an urgent and unusual situation. I think Finland should have some room to maneuver in drastic and unusual situations. Whether Palgi's situation is warranted urgent and unsual is probably arguable. I think from the perspective of the police, they probably thought that lots of young people run off to a friend's house after a night of drinking or maybe ran off with some girl for the night, etc. In that case, waiting for a day makes sense, but 3 days really is quite a bit especially in current times when everyone has access to phones and internet and can get in touch in almost any situation.