The characters think out loud because that's how the manga was drawn, the anime just copied the source material, and if they are not doing that there's no way of knowing what's happening because there are no speech bubbles, you're not reading a research paper mentioning only the facts, it's supposed to be the internal thoughts of a person, so the prolonged "should i do this? will he realize? will it be obvious?" etc... is natural, no human thinks in bullet points, it would actually be too unrealistic, plus there are some subtle moments in Death Note, saying there is a complete lack of sublety on it is intellectual dishonesty.
Also having these thinking out loud moments doesn't remove the brilliant moments in the series.
One of the compelling points of Death Note was that Light started off as someone with good intentions, but let power go to his head. He seemed like a nice, moral person at the beginning of the story, but that changed over time. That's what made him interesting as a main character and a big part of why the series was so sucessful. You see stories from the perspective of the good guy all the time, but it's not every day that you see one from the perspective of someone like Light.