Lumber harvesting is the most dangerous profession in the US but I imagine that most deaths would be described as "accidents". For example, someone cuts a leg with a chainsaw, a tree snaps in a weird way, someone gets pushed off a cliff.
Police officers, on the other hand, usually due to violence while interacting with other people.
In other words, a lumberjack, roofer, etc could think that they won't die today on the job because they are being careful, because there are safety protocols set by OHSA, etc. The same might not be true for police officers because there is little that they can do to address how others will interact with them.
In a sense, police officers might process their job more closely to how a soldier process their job than a lumberjack/roofer.