A lot of... Passionate... posts in this one.
I think many situations make it wise to announce your presence and the fact that you are armed and prepared.
Sometimes the home invader did not think the dwelling occupied and will choose escape on his own once they know someone is in there.
Also, when you announce that you know that someone is in your home and they do not respond you have additional data on your situation and can adjust your plan accordingly. It can be an important part of identifying the target.
"I know you're here, I am armed! I've called the police!"
"Agarn, it's me, Bill..."
Vs
"I know you're here, I am armed! I've called the police!"
[Silence] or threats
My research and study suggests that if you are actively in a fight for your life, maintaining your silence makes perfect sense.
Prior to when the fight starts, it makes sense to try to deter the conflict.
I don't suggest standing in the worst defensible position in your home when you make the announcement, but there is certainly a case for announcing your presence and preparedness