I don't see what relevance the fact the guy didn't die immediately has on the way the police dealt with it.
I was responding to your post, are you really not getting this, it was a simple point that really doesn't need several posts to explain - you said:
A man died in his house, apparently as a result of his actions, I'm not surprised the police arrested him.
that isn't the reason they arrested him, the man didn't die in his house, he fled down the street and was taken to hospital
they didn't arrest him because a man died, they arrested him for GBH because he stabbed someone... the man later died later in hospital and he was re-arrested... but he was already under arrest at that point.